Twittelator is the best all-around free twitter app I’ve found for the iPhone.  It allows you to do custom searches and it saves the search each time you do a new search. It gives you quite a few different categories of tweets to browse, which Twittelator calls Groups, including featured Tweets, your own tweets, friends’ tweets, everyone’s tweets, favorites and more.  It gives you twitter profiles with stats too.You can not only use follow, unfollow and favorites from this app, but you can also bookmark twitter accounts that you aren’t sure you want to follow but you want to be able to find again.  The one thing it seems you can not do easily is retweet.

Features:

1. Shoot, Edit and Upload Video tweets (requires iPhone 3G S)
2. Cut, Copy, Paste
3. Shake to undo composed tweets before publishing
4. Paste an image from another application into your tweet
5. Email tweets and links without leaving the application
6. See street map, satellite map or hybrid map of the location of any tweeter
7. Set your location as a placename accurately using Google’s reverse geocoding
8. Simple search mode (just enter words)
9. Tap & hold 2 secs to save any set of tweets
10. Read tweets offline
11. Tap/hold a tweet to add to Recents this session
12. Add any user to Bookmarks
13. Block and Unblock any user
14. Set autorefresh interval to 2,3,5 or 10 minutes

According to the info icon in the free version of Twittelator, Twittelator Pro has even more features for those of you that don’t mind shelling out a few pecos.  Pro gives you the ability to use dingbats and upload your location and search nearby.  The most important feature is that it allows you to control multiple twitter accounts on your iphone.  It also allows you to email and retweet tweets unlike the free version.

Twittelator Pro is $4.99 in the iTunes app store.