I like Tweetie on iPhone. On my desktop I use the incredibly uncool, plain old web client :-) One of the reasons is that many of the RIA twitter clients don't handle Japanese characters and I occasionally use Twitter as a communication and learning tool for the language.
After a thorough tweeter client investigation procedure :), I am currently happy with Chromed Bird, which is a tweeter extension for Google Chrome browser. It is unobtrusive and keeps a live count of new tweets - simple and quite useful.