** Update ** and another native iPhone twitter client called Twinkle. The difference with this over Mobile Twitter below, is that it also adds in location allowing you to see tweets from people within 1,2,5,10, and 50 mile radius of your current location. Add "www.polarbearfarm.com/repo/" to the installer app.
I posted a while back about a couple of native S60 and J2ME clients for accessing twitter/jaiku and recently I've been playing with a native iPhone twitter client developed by npike.
Add this resource to installer http://apps.npike.net/repo.xml and then download the twitter client from the Npike directory.
Clean and simple UI. I like.
Here's some other twitter based resources for desktop, browser and mobile.