Sorry 3rd party apps, it's been nice, but now that the official twitter iphone app has been updated to 3.2 with push notifications, I'll be removing you.
I somehow managed to miss this this last weekend, but Seesmic is now available for the iPhone and Touch / iPad, etc.
The "official" twitter client release of the previously named "Tweetie 2" is out, and Twitter for iPhone. The icon change is a bit strange to me (it's now blue instead of silver), but other than that it's mostly the same. Some cool stuff for when you're not logged in, and the search screen is a bunch nicer, but other than that it's mostly the same old Tweetie (which isn't a bad thing, as that's my 99% go-to app for twitter on the iPhone). Review and screenshots in the linked article.
The Seesmic twitter client has added support for userlists. Works pretty nicely, and looks good. Tweetdeck is still my desktop app of choice, but hey, different strokes for different folks.