I can't tell you how many Twitter apps I've tried on the iPhone. I went through at least 5 or 6 before I got to TwitterFon, which I've now been using for the past several months. Does it have every single feature you could imagine? No, but I'll bet you'll find it has everything you need.
What do I love about TwitterFon? First, it's free. OK, I'm a cheapskate, but still, TwitterFon stacks up well against any of the paid Twitter iPhone apps. Second, it's fast. No matter how many tweets I'm behind it seems to load them in no time at all. Next, as with all good iPhone apps, the user interface is intuitive. The developers managed to put all the right controls on one screen without it seeming overly crowded. Then there are the nice, subtle touches, like how you can quickly get to a hot Twitter topics list from within the search screen.
Others have complained that TwitterFon doesn't support multiple Twitter accounts. I suppose if I was working with more than one Twitter account that would be a drawback, but I only have one.
If you're looking for a great, simple and free Twitter client for your iPhone you can't go wrong with TwitterFon.