1. Blu Client - If you're looking for an application that is easy to use and help you manage all your conversations of Twitter while not taking up too much space on your desktop, Blu is for you. It's rectangle shape looks similar to the AIM instant messaging system. It features a muted blue and white design that looks both simple and sophisticated at the same time. Blu lets you see @replies and mentions in a conversation view, which makes it easier to understand them in context.
2. TweetDeck - This is the perfect app to use if you have multiple Twitter accounts. You can personalize your "deck" to have your home page or mentions in any particular order you'd like. For example, if you had two Twitter accounts (@ComputersRFun and @ItsLaptopTime) you could set up your deck to have the mentions of both accounts next to each other, and then only the home page for @ItsLaptopTime on the right side. TweetDeck is a great organizing tool and has a great feature of allowing you to tweet one thing from multiple accounts.
3. HootSuite - Many people use different social media networks besides Twitter, including Facebook and Google +. HootSuite is an application that allows you to manage all your social media networks all in one place. Hootsuite organizes your social media accounts into tabs, and within those tabs, it displays information in streams. This is available in two plans: Basic (free version) that includes five social profiles and two RSS/Atom feeds, and quick reports, and a $6/month plan that includes unlimited social profiles, one free team member, one free enhanced analytics report, integration with Google Analytics and Facebook insights, and the ability to save tweets. I would recommend starting with the Basic even though it's ad-supported. If you like it, then you can pay the $6/month for extra features.