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I've tried a few free ones...Tweetdeck, Twitteriffic, Twitbird, Echofon. I have a couple of accounts so Tweetdeck was great because I could load all of the accounts. Echofon was the latest one I used. It's ok, but I don't like that I can only use one account. I never tried Tweetie because I didn't feel like paying for it.
 
I haven't seen a single person mention Twittelator Pro. I don't Tweet a lot...but I follow quite a few and Twittelator is the best I've used. It has a great UI and it's very easy to get to the links.

Twittelator Pro also gets one of the best ratings on iTunes for any of the Twitter client.

4.5/5

There is a lite (free) version but I've never tried it.
 
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