Twitter

Also see Social Media 

FollowerWonk
Show you when your Twitter follower are online so you can plan accordingly. Analysis by region. But reports can take hours to build. Free but more metrics with paid account.

Free Twitter Designer
Easy-to-use image editor to help you create a professional-looking theme on your Twitter account.

Kurrently
Search engine for Facebook and Twitter.

ManageFlitter
Finds relevant people for you to follow. Allows you to sort your followers/following lists by how much the people following you tweet, whether they follow you back and if they have a profile picture. Select a group and unfollow with one click so you don't have to unfollow each account individually. Schedule tweets based on when most of your followers are online. Find out who has unfollowed you. Manage multiple Twitter accounts. Track keyword mention. Some features are free but to get the most out of it you need a subscription of $12 a month.

MyTweetSpace
With minimal effort, create a Twitter background, badges, add graphics, play with text. Log in with your Twitter account and it will automatically update your background.

Plume
App for Twitter users. Customizable options. Free for Android, $3 for iOS.

SocialBro*
Helps businesses manage and monitor their Twitter accounts, discover key influencers, schedule Tweets at the best times, track engagement, and analyze competitors. Free Trial with pricing starting at $13.95. Video explanation.

Topsy
Search content published on Twitter and the web, and sort it by date or relevance. Use it to find influencers in a certain subject area.

Tweet Beep
Get email alerts whenever somebody tweets about something you're interested in--even keep track of who’s tweeting your website or blog, even if they use a shortened URL. Free account available or paid account at $20 a month for more options.  Video explanation here.

Tweet Chart
Allows you to generate a report of custom data for anything you can search Twitter for: hashtags, words, phrases, usernames or URLs. A reporter could determine which hastags were used most frequently in the past week, deciding to, for instance, report on a recent crime spree or a particular local event. Free.

Tweetbot 
Mac app with customizable options. View threads showing co-worker tweets only, for example or retweet from multiple accounts. $3.

TweetDeck*
Look at multiple Twitter feeds on your desktop. Powerful filters help you focus on what interests you. Schedule Tweets, set up notification alerts for new tweets. Option to have it ask for confirmation before a tweet goes out--giving you another chance to avoid sending something inappropriate or not well-crafted. Bought by Twitter in 2011.

Tweepi
Cleans up your Tweeter feed--removing inactive followers in bulk and other Twitter management chores. From $7.49 a month.

Tweet Level
Allows specific searches for hashtags to determine trends by watching a topic's buzz level or to evaluate the user's social influence. You can also evaluate the buzz around a certain topic to determine if it’s a trend worth paying attention to.

Tweet Reach
Lets you see how far your tweets travel and determine the effectiveness of your social media campaign. How many people your messages reach, how many tweets it took to reach them, how many times your tweets have been shared by retweets. 

Twellow
A directory of Twitter users. Lets you search for people based on their name and the information they put into their bios. Find people with similar interests to follow.

TwitPic
Trending photos and videos on Twitter. CLOSED SEPT 2014.

Twit Scoop
Realtime tag cloud of what is hot on Twitter right now. See what the leading subjects of conversation are on Twitter. Especially helpful whenever there is some big news event taking place.

TwitterBioGenerator
A canned description of you is a mere click away!

Twitter Feed
TwitterFeed to automatically fetch the latest entries from an RSS feed of your blog or website and send them as tweets through your Twitter account.

Twitter Search
The search engine for Twitter. See what people are saying about your competitors by to:competitor replacing competitor with Twitter handle.