On iPhone, "Twitter for iPhone" (used to be Tweetie 2). I'm actually happy with that one.

On Mac, I keep going back to Tweetie, but it's incredibly old and busted now; can be really annoying. I also periodically flirt with Echofon, YoruFukurou and Kiwi. Of those, probably Kiwi is my favourite.

On iPad, I mostly use Twitterrific. It's not perfect, though; it doesn't autorefresh and (critically) it doesn't even attempt to check if I have mentions or DMs unless I explicitly switch to those timelines, which is a bit of an antiquated approach these days. TweetDeck has a horrible UI and isn't as stable, but it does let me see my followees' timeline and my mentions simultaneously. Twittelator has a very fun UI, but it sacrifices vast amounts of screen-space just so it can draw all the cute surroundings, and that gets grating after a while.

The only platform on which I'd say I'm actually happy with my chosen Twitter app is the iPhone. Jury is still out for Mac and iPad.