Top Twitter Applications you should know

Twitter has been expanded with simple utilitarian features, widgets and services for greater efficiency in search and also creating photo albums.
Top Twitter Applications
Apart from the recent Twitter makeover, these are some of the top Twitter applications that can make Twitter a better hangout place:

Send tweets directly from Google Talk
Chitter.im lets you send tweets directly from Google Talk. Sign in using Gmail ID and allow the app to get access to your Twitter account using OAuth. The messages that you send through chitter.im on Gtalk will automatically be posted on your twitter profile.
  
Tweets longer than 140 characters
Twitlonger.com allows you to post messages longer than 140 characters on Twitter.  There are lots of situations where you cannot convey a message in 140 characters, in which case, Twitlonger helps.  You just need to type your message and post it. Half of your tweet will be displayed followed by a link to the entire tweet.

Find out if someone unfollows you
Tweepi.com can help you flush out people who haven’t followed you back. You can also copy & paste usernames and follow them at once. Cleanup tweeples who you think are inactive or overactive, follow your followers/ followers of any twitterer. Tweepi also displays real time stats which makes it lot easier to use.  
  
Custom Twitter backgrounds
Freetwitterdesigner.com lets you create a personalized twitter background with customized text, images and color. So if are too lazy to customize designs using Photoshop or other editing tools, then this app is for you.

Manage Twitter with the following applications
Tweetdeck is an awesome app. One of the most versatile app with an user friendly interface. I would personally recommend this if you’re an absolute twitterer. You can organize your feeds, filter tweets, schedule tweets, manage unlimited accounts and get tweet notifications. Its compatible with almost all the operating systems (Yes it’s a desktop application).

Twitterrific is now a single, universal app that is a Mac OSX and iOS exclusive Twitter client. Twitterrific can be used for free with ads and a single account. Purchasing the in-app upgrade gets you more. Specific new 3 features include interface optimization for Apple's new retina display, the addition of a light theme (via the Settings App), VoiceOver support for the visually impaired, OAuth authentication for all new media services and a host of bug fixes.

Hootsuite allows you to multiple social profiles like Twitter, facebook, Google + and LinkedIn. It also lets you schedule messages & tweets, monitor mentions, and analyze social media traffic. You can customize the Hootsuite Dashboard. However, this app comes with a 30 day trial version.