Here are some of the top Twitter clients for Linux.  I have tried each of these on Ubuntu 9.10 and each have their downsides.  They all run pretty well, with the exception of Twitux.  It seems to have some memory leak problems.  If you leave Twitux running all the time it will consume large amounts of memory over time.

Gwibber – My choice of twitter client.  This client will work with Facebook, Twitter, Identi.ca, Flickr and a few others.

Seesmic – Adobe AIR Twitter client

Pino – Twitter and Identi.ca client

Qwit – Twitter and Identi.ca client

Twitux – Basic twitter client, hasn’t been updated in a while and seems to have some memory leaks.