Twidroid
I've tried many upon many Android Twitter clients, and while Seesmic is nice.. it's slow and ugly... Many others don't support video, or photos, etc.
My favorite twitter client absolutely is Twidroid (Pro). I have a hard time getting myself to spend more then $1.99 USD on a phone application, but I purchased Twidroid Pro just the other day so that I no longer would need Twidroid for most things and Seesmic for video uploads.
Twidroid pro is fast, easy, reliable, and kind of pretty =)