Because I like the way that Tweetdeck allows me to create columns of different items of interest, from searches to user lists (and integration with Facebook), I like Tweetdeck (and Tweakdeck, which is a slightly, well, tweaked version.) If it comes to pure twitter, I like Plume. I really don't like the official client myself - it's slow and laggy, and, on a device like the D3, with a 1 GHz CPU running 512 MB of RAM, that's rather inexcusable. I think it's just a sloppy app. Others, of course, may disagree...
A lot of people like Tweetcaster, but I think it looks like eye candy (and I mean that in a not very complimentary way.)