Here's the honest truth: finding good apps takes work. The best ways to do it are to link in to a group of like-minded people via twitter or subscribe to RSS feeds that are experts in the genres you're looking for. Then filter by iPhone app. Developers are frustrated because of the signal-to-noise ratio is so high, and Apple's people have no idea how to parse and promote, so there are literally thousands of developers tearing their hair out, my cousin being one of them.
So listing a group of "best" iPhone apps is like listing a group of "best" songs. It's so diffuse as to be meaningless. You need to find your passion first, then see, in the parlance of our times, if "there's an app for that." Instead of looking at solutions, you should be looking at interests and opportunities. There the magic lies.
Finding the right iPhone app is like good sleuthing. You can't rely on lists, or promotions, or rankings, because the definition of what a good iPhone app is keeps changing. If you look at the apps that came out when the App Store debuted, there wouldn't be a single one that you'd be proud of today. Apps are disposable things, even the useful ones. So when you look for "good" apps, you're really looking for the one you want right now. You don't need iPhone apps, because you were getting by just fine without the Jesus Phone.
Apps are personal, and specific. The best developers understand that, and don't put out stuff like iFart. So, the best way to look isn't hey-I'll-try-the-free-popular-ones or going by Apple's Hot News releases. It's by asking yourself what you want a phone to do, and find a developer who shares your vision. Then follow them relentlessly.
Better yet, make your own. Because six months from now, we'll be astonished we put up with crap like this.
I know this isn't a convenient list, because it's more complicated than the question appears: it's truer than a series of pat answers. Apps are a personal thing. Everyone knows about the Google and Facebook apps. Nobody knows about the terrible dreck that deserves to be shot. Your mission is to find the golden, personal, useful, beautiful layer in between. (since we're not complete sadists, may we also suggest the following:
Appsniper,
Appbeacon,
Apptism,
Unofficial Apple Weblog,
Ars Technica,
148Apps.)