TweetDeck - helps me to follow the conversation on Twitter and see my direct messages, messages, tweets from my friends and others - all those in four categories on one screen. It also allows me to find users, follow new ones and of course - tweet and respond to messages. All in few seconds!
Advanced Twitter Search - is good for specific searches, mainly when I am writing posts on a specific topic and need more info.
TweetBeep - I could not live without it, as much as I cannot imagine living without Google alerts. Using this tool I can get all the relevant information (with or without URLs) into my gmail inbox daily and read through it during lunch time for instance.
Twitterlocal - useful in locating fellow users, mainly before and after events.
Tweetstats - time to time I like to look at the trends and doublecheck (in responses column) if all my responses were noticed. For some reason Netvibes and web still come up as my main Twitter interfaces, whereas I am using Tweetdeck and HelloTxt, no idea why:/
And last one, quite a recent discovery - Monitter - brilliant for finding real-time tweets on three different keywords.(see below)
Well, I guess that's it. I bet my fellow bloggers are using much more, but for me those are main tools, and as for now, I am quite happy using them. Unless you have something better for me;)