TwXplorer is a free social-media research tool by the Knight Lab for searching Twitter in order to understand the global conversation about a topic. For any search terms you enter, you get four different ways to see your search results:

  1. Up to 500 recent tweets containing the terms you entered.
  2. In tweets that include your search terms, a bar graph showing the most popular other words that appear.
  3. The most popular hashtags included in tweets containing your search terms
  4. The most popular links in tweets containing your search terms

SocialBro for Chrome app lets you manage and analyze your Twitter account by monitoring your activity and your current and new followers. Free.

BackTweets allows you to find all the tweeted mentions of a specific link, hashtag or Twitter handle through a simple search. Free.

Twopcharts tracks and ranks the most influential Twitter users based on location and language. Once you’ve selected a location and language category, Twopchart provides charts of users with the most new followers, most tweets or most seniority within that category. Twopchart provides other helpful searches including details of specific Twitter handles, comparing followers or followings of different users and the first 100 tweets by a particular user. Free.

Followerwonk analyze and grow your Twitter network by helping you better understand your current followers, connect with new influencers, and compare your results with others. Free.

Social Rank analyzes your Twitter followers to determine who are your most engaged and most valuable followers, and who are the best of both. Free (or $25 per month upgrade to Premium).