There a number of software available for using Twitter from the desktop. Most of them are complex, not so much user friendly and lack in features. Some of them requires Adobe AIR, some are not supporting multiple Twitter accounts.
Echofon supports multiple twitter accounts. Account switching is very easy and notification are shown in background for mentions and messages you receive in non-active accounts. You can search for anything as you do in Twitter and can even save the search.
When you click on a user or conversation, a detail window will open allowing you to read the conversation, or see all of that users information including tweets, favorites, lists, re-tweets.
It supports keyboard shortcuts so you can do Ctrl+K to mark all tweets as read or Ctrl+R to check for new tweets in your timeline. Ctrl+I can be used to include a picture in your message while composing a tweet.
Here is a screenshot of the application interface.