I believe this is the best, most complete and accurate list of valuable Twitter applications available on the internet right now.

To be fair, I absolutely have merged and plagiarized other older and outdated lists that I found (the larger ones are credited below). However, I spent a good deal of time to clean out the dead applications, delete the apps that were overly quirky or being developed, focus more on the apps that increase productivity, and add in many of the new great apps that have come out over the past six months - particularly in the productivity / business apps section where my primary interest lies. I have also tagged the tools that cost money / have a premium option ($) as well as if they have a valuable free option (F/$).

Finally, while application selection can be a personal thing, I tagged my favorite app (*) in each category.

I will try and update this list over time, but you can be assured that as of May, 2011, every site on this list has been tested and is up and running (or tagged as being in beta/alpha). I don't guarantee that the apps all work, but the sites were definitely up and running. Please e-mail me or add a comment with any new apps or corrections you find that you'd like me to add.

Simple Web Based Clients and Twitter Viewing Tools

1. Twitter.com (*): Can't go wrong with this -- web, iPhone, etc.
   
2. Twalala: On-line browser beta Twitter tool that allows you to filter out / mute tweets you wish to ignore.
3. Hahlo: Another good web based and iPhone optimized site where you can view tweets and tweet.
4. iTweet: Similar to Hahlo - auto updates.
5. TwitStat: Mobile web client (supposedly has analytics, but I didn't see it)
6. Dabr.co.uk : Another mobile web client
7. Splitweet: allows multi account Twitter management.
8. Twimbow: In alpha, but seems like an interesting web based browser if you can get an account.
9. TweetVisor: Interesting new activity based web twitter client
10. Twazzup Reader: Good web based Twitter Client
11. Accessible Twitter: Twitter UI optimized for disabled users and intended to be easier to read.
12. Qwitter Client: Accessible Twitter client designed for access by the blind via a user's screen reader.

Directory And Top User Search Tools

1. Just Tweet It: A twitter directory sorted by interest
2. Twitaholic: Similar to WeFollow - Lists top 1000 Twitter Users by followers.
3. FameCount: Active users on Twitter, Facebook, and YouTube
4. Twitrank: List of top 150 Twitter Users By Followers, People They're Following, and updates
5. Twellow (*): The Twitter Yellow Pages -- Find people by area of expertise.
6. We Follow: Find celebrities and follow-up people and key areas of expertise.
7. Tweetfind: Twitter Directory with Social Listings, Twitter Lists & Tools
8. TwitterPacks : Answers the question: If someone were joining Twitter today, who might they follow?
9. Start4all: Directory of Twitter related web pages
10. FollowerWonk: Search Twitter Profiles By Keywords / Sentences. Can compare two users as well for overlap
11. Twiends: Tool to grow your Twitter / Facebook / YouTube following by trading likes.
12. Fan Page List: Social media directory of Twitter & Facebook Brands / Celebrities / etc.
13. Increasr: Very similar to Twiends, a Twitter follower tool
14. FollowFriday.com: Ranking of the most recommended Tweeps
15. FriendLynx: Find Your Facebook Friends On Twitter
16. FilterTweeps: Advanced Tweeps Search Engine
17. Resonances: Influential Tweeps Directory
18. Local Follow: Tweeps Search Engine

Track The Latest Trends and Tags

1. Hashtags (uses Trendistic data): Shows graphical 7 day trend on keywords and names of people that used that keyword.
2. Serendipitwiterrous: Search for tweets of a certain person using certain keywords
3. Trendistic (*): See trends in Twitter - trending tags, 24 hour, 7/30/90/180 day graphs
4. Twitscoop: See key trends and events on Twitter -- post Tweets in response.
5. TwitLinks: The latest links from the worlds top tech twitter users.
6. Tweet Scan: Show top and search keywords.
7. Tweetmeme (*): Good site to see the latest and hottest stories / images.
8. Twemes: Worldwide tags & Trends (Twemes)
9. Monitter: Twitter monitor which watches up to 3 keywords in separate columns in real time.
10. Twistori: Quirky live stream of Tweets showing loves, hates, believes, wishes, etc.
11. Twitturls: Find out the latest URLs posted on Twitter
12. Twitturly: Similar to Tweetmeme - latest and hottest stories / images.
13. Twendz: Explores Twitter Conversations and Sentiment
14. Topsy: Real Time Search For Twitter
15. Sulia: The Interest Network - See top headlines.
16. Favstar: Favorite funny tweets
17. Twazzup: Realtime search results from Twitter
18. hashMASH: Finds and sorts similar hashtags based upon activity
19. SearchHash: Download range of tweets based upon hashtag
20. Hashtagify.me: Explore Twitter Hashtags and their relationships

Segmentation and List Grouping Tools

1. Formulists (*): An excellent app that will help built personal lists for you based upon certain criteria / keywords.
2. Group Tweet: Tweet with only a particular group of people
3. Crowd Status: Create and find out the status of a certain group of people on Twitter
4. Twitter Groups: Tag your followers into different groups. Send a message to the entire group at once.
5. Triberr: Interesting site that will retweet everything in the groups you join.

Twitter Utilities

1. bit.ly (*): The King URL shortener - many twitter apps use bit.ly directly or can leverage their bookmarklets
2. Ping.fm (*): Extremely valuable service that lets you publish your updates to many social networks at one time.
3. Visibli: Nice engagement bar that shows your brand above links you share. Also has analytics.
4. Tweet Burner: Track the links that you post on Twitter - URL Shortner
5. Twitter Split: Interesting script / tool you can install to allow you to track links in tweets you post.
6. TrueTwit (F/$): A Twitter validation tool that helps automate some key services. Free and paid services are useful.
7. Twit Longer: Allows you to send longer Tweets
8. Twitter Keys: Blog Post & Bookmarklet with little icons & images you can add into your tweets.
9. Mokumax: Nice free app to schedule branded tweets
10. TwimeMachine: Way to see all your past Tweets
11. Follow Friday Helper (*): Let's you easily build thank you & other messages to people who mention, RT, etc. you.

Integrate Twitter with Files, Images and Videos

1. Twitpic (*): Share photos
2. Twitvid (*): Share photos and videos
3. Autopostr: Update your Twitter when you post a Flickr picture - In Beta, no invites available.
4. Twixr: Share pictures on Twitter via your mobile phone
5. Twixxer: Share photos and videos on Twitter
6. MobyPictures: Share your images across multiple sites including Twitter

Twitter Background Sites

1. Twilk ($) (*): Cool site that Create a background image of all your followers / who you follow. Paid takes out advertising
2. Twitrounds: Another Free Twitter Background Tool
3. Twitbacks: Create free twitter backgrounds.
4. Free Twitter Designer : Free Tool To Design a Twitter Background
5. Twitter Images: More free images
6. Twitter Backgrounds.org: MORE free images
7. Twit Background Images.com: MORE
8. Twitr Backgrounds: and more.
9. Twitpaper: More.
10. Free Twitter Layout: oh, and more
11. Tweativity: Windows based app for Twitter backgrounds.

Summarized Reports / Digests Of Social Activity

1. Gist (*): A great app that tracks activity and tweets for your contacts across all social platforms. Integration with Outlook, iPhone, Android, and more. Definitely worth a look.
2. Nutshell Mail: Delivers a nice daily e-mail report of your Twitter, Facebook, and Social Media Activity.
3. Twilert (*): A good free app that will provide a daily digest of tweets via e-mail of search terms & people
4. Tweet Beep ($): Keep track of conversations that mention you, your products, your company, anything, with hourly updates via keyword tracking.
5. Stream Spigot: Creates a digest of tweets for a person or list delivered via RSS or a web page you can visit daily.
6. Social Oomph (*): This is also listed below as a paid app, but the free version gives you a nice daily summary of Twitter Activity by keyword / user.
7. ChiliTweets ($): Finds "hot" links and tweets and aggregates them for you

Cool Ways To See Your Tweets And Followers

1. TwitterFountain (*): Very cool way to view tweets by person/ keyword in real time on big screen (trade shows & events).
2. TwitterCamp Nice way to view tweets on a big screen or monitor
3. Twit100: Provides a unique view of the last 100 tweets from your followers.
4. TwitArcs: Interesting visualization tool to see how a user's tweets are connected
5. Twitter Spectrum: Visualization tool that shows how two keywords are connected via Twitter keywords.
6. TwitterBrowser: Lets you browse ones friends graphically.
7. Twitterfall: An interesting real time browser of Twitter activity by keyword / user / etc.
8. Twylah: An on-lin Flipboard type view of your Tweets. In Request only Beta - Here is mine.
9. MentionMap: Very interesting "mindmap" type view of mentions by username.

Follower / Unfollower Tools

1. Does Follow: Simple tool to see if one person follows another person.
2. Manage Flitter ($): Clean up and manage your followers. Also has some analytic stuff.
3. Tweeter Karma: See who you are following that is not following you and visa versa. Can mass follow those you don't follow.
4. Qwitter ($): Get a daily report showing unfollowers. (I could not get this to deliver info to me)
5. Twerp Scan: Interesting way to drill down into who you or your followers are following.
6. Twitspam: Track and Report Twitter / Social Network spammers
7. Is Now Following: Tracks when you add new followers and tweets it
8. Fllwrs: Keep track of your followers / Unfollowers
9. Twitoria: Shows activity of the people you're following to stop if they haven't tweeted in a while.
10. FollowCost: What's it "cost" to follow someone (how frequently do they update / tweet)?
11. Just Unfollow: Unfollow those that are not following you.
12. IsFollow: Find out who is following who by entering in two usernames.
13. Tweet Find Tools: Good free tool to unfollow people that don't follow you. Also has tweet scheduler
14. Friend or Follow: Another app to see who doesn't follow you and visa versa.
15. Tweepi: Another list cleanser
16. Who Unfollowed Me: Find out who unfollowed you.

Twitter Account Analysis tools

1. TwentyFeet (F/$) (*): Excellent summary of stats across multiple sites. First Twitter & Facebook account are free.
2. Klout (*): An excellent app to track and rate your social media activities (Facebook & Twitter, LinkedIn to follow).
3. Empire Avenue: Similar to Klout - only more complicated with a "virtual investment game" built in.
4. Crowd Booster: Another good analytic tool
5. Peer Index: Another good analytic tool
6. My Tweeple ($): Twitter Account Evaluation Tool. Follower counts, ratios, tweet counts. Review Recent Tweets (See what your followers are saying), Follow-back, hide or block new followers. Create Tags, Notes, and Share. Good tool to export your entire follower list to a csv file.
7. Twitter Counter: Good Twitter Analytics / Comparison & Statistic Tool. Also has some good blog scripts and Twitter Tools
8. Twitter Grader: Analyses your Twitter account on a 0-100 score. Computed based on how complete your profile is as well as the number and influence of your followers. Also shows top users in categories. Good basic stats.
9. Tweet Stats: Graphical representation of your Twitter activity including time of day posting, interface used, etc.
10. Tweeple Twak (in alpha): Supposedly track your friend gains and declines. Site is up, but can't see what it does.
11. Twit Graph: Similar to TweetStats, but weaker and has more advertising
12. Twoolr: Another Twitter Analytic Tool
13. Twitter Ratio: Find out your friend to follower ratio.
14. Retweet Rank: Provides a ranking on the number of Retweets You Have
15. See Tweeb and SocialDash Under the iPhone Apps section for a few good iPhone Apps that provide statistics
16. The Social List: Ranking Tool to compare yourself to others via Facebook, Twitter, LinkedIn, and 4sq
17. SocialBro: A very interesting new desktop app to look at Twitter Statistics - in Beta, but very cool.

Business Social / Twitter Suites & Tools

1. MessageMaker ($$) (**): A shameless plug for my company's (One To One Global) product that is designed for organizations and companies to deliver messages to tens, hundreds, or thousands of social endpoints (Twitter, Facebook, etc.) and then provide amazing aggregated reporting. Fantastic for companies with multiple brands, franchises, and organizations looking to leverage their sales team's or employees. Contact me if you're interested in learning more.
2. Pluggio ($) (**): One of my favorite personal apps to help find valuable content, schedule tweets, and get reports on your activity. Free version is ok, paid version is justified.
3. Tweet Adder ($) (**): PC & Mac tool to help build a targeted list of followers and un-follow those those that don't follow you back. Sends thank you messages to new followers. On my must have list.
4. NEW: Tweet Attack ($) (*) : Similar to Tweet Adder, but seems like it brings some new things to the table. I included a discount link I found.
5. Tweet Whistle ($): Similar to Tweet Adder as well. Mac and PC version to build your followers.
6. Twittenator ($): Similar to Tweet Adder. Seems solid, I've just become used to the other.
7. Sprout Social (F/$) (*): Easy to use dashboard to manage your social efforts with attractive analytics.
8. Social Oomph ($$) (*): A complete Twitter Automation and Analytic Tool. Free version also very valuable for keyword analysis reports, follow backs, and reporting.
9. Timely: An interesting app that analyzes and schedules Tweets based upon the best time to deliver them
10. Tweetag: Browse tweets via tags and receive e-mail notifications.
11. Tap11 ($): Real-Time Intelligence and Engagement Platform for Twitter & Facebook
12. Twaitter ($): Social Media Suite handling scheduling of tweets, statistics, other info.
13. Twollo ($): Targeted follower building tool based on keywords with auto-follow
14. BufferApp ($): Similar to Pluggio in that you can build a targeted list of tweets that it will intelligently deliver over the course of the day.
15. Radian6 ($$): Very valuable monitoring and Analytic Tool
16. TweetBig ($): Another good suite with auto follow-back, tweet scheduling, analytics, and other stuff.
17. CoTweet (F/$): Tool to help empower teams to monitor and engage with customers across multiple accounts
18. Mutual Mind.com ($): An enterprise level social media management platform
19. TweetSpinner (F/$): Manages followers, rotates profiles, archives and schedules tweets.
20. TweetBot / Tweet Scope: Similar to Tweet Adder - with auto unfollow and DM capabilities.

Twitter Integration With Your Site or Blog

1. Add Tweets: Make Twitter Update Widgets for site or blog using javascript
2. Feed Tweeter: integrate Twitter with Plurk, your blog and delicious
3. Follow Me On Twitter Buttons: Follow me on twitter buttons
4. Loudtwitter: Ships your tweets to your blog.
5. PingTwitter: Automatically update your Twitter Account when you publish a new blog pos
6. Siah Design: Free Twitter buttons and animated GIFs you can use.
7. Stammy's RSS To Twitter: Not too many people have access to a Ruby-enabled server so the author decided to make a simple PHP script to get the job done.
8. Twignature: A decent translated Japanese app to take your username and create a usable Twitter signature for websites & e-mail.
9. Twit This: Add this option so people can easily tweet information from your site or blog
10. Twitter Tools: A wordpress plugin that lets you integrate Twitter with your blog. You can send your updates to your blog as well as create tweets directly from your blog
11. Twitter for Wordpress: Script displays latest tweets on your blog
12. Twitterfeed: Post your blog to Twitter through your RSS feed
13. Twitter Updater: Automatically sends a Twitter status update to your Twitter account when you create, publish, or edit your WordPress post
14. Twitter Wordpress Sidebar Widget: A wordpress widget where you can send your tweets to your blog
15. TwitGIF: A translated Japanese app that creates an animated GIF from your latest Tweets.
16. Chirrup: PHP Script that allows you to collect Twitter comments for your site.
17. Dlvr.it: Deliver Your Blog To Twitter, Facebook, and More
18. DiggDigg: One of many Wordpress plugins that integrate social sites.

Once again, I credit the following posts for providing some of the information I used here. However, these posts are old, have many dead links and are missing many of the best new apps that are out there.

http://www.squidoo.com/twitterapps
http://eonlinetips.com/200-twitter-tools-list-even-your-mom-would-love-it/
Credit to the people on this LinkedIn Thread as well:
What are your favorite Twitter tools? | LinkedIn http://linkd.in/jUu6yX

Now that you have all these tools to use, be sure to follow me @ericsgoldstein and continue to read my blog here.