This is the tool I have been using the longest. It has a free version and an upgraded Pro version. The free version has many good basic features and is good enough to manage less than 5 social profiles from a single platform. The free version allows you to schedule tweets for a later date or time, however, for bulk scheduling, you need an upgraded paid version.
You can list your contacts with the number of their followers, following and their Klout score. You can perform all the functionalities you can do using Twitter, i.e., follow, unfollow, report, block or list the user using this tool, but in a better way. You can also view stats for a specific date range, the last 7 days, 24 hours and so on. This tool has much more to offer and is worth checking out - I have been using it since.
This is similar to Hootsuite that allows to to manage your social profiles more efficiently. It launches as an independent browser. For use in a personal computer, there are two versions: desktop and chrome. Additional functionalities include, filtering each column by text, identifying popular tweets and clearing seen updates in each column and so on. It also 'pings' with a small popup when new tweets come. Translating updates and auto-URL shortening when you compose are pretty cool too.
I started using this tool fairly newly but I find it very useful. It has some features similar to Hootsuite - scheduling tweets, URL shortener and click stats. However, it has some cool features that Hootsuite doesn't have and it is for those that I use it. It shows a followers, followings, tweets and DMs in graphs plotted over time that clearly indicates how your twitter profile has been growing/shrinking over time. A warning though is that the figures aren't as updated as in other tools providing the same graph (below).
Other interesting features include vetting your followers, composing and scheduling direct messages for your new followers, specifying criteria to automatically unfollow certain people and so on.
Though it has other functionalities, I use this tool just for the stats - the graphs that show the increase/decrease in twitter followers, following or tweets or mix of followers and tweets in separate graphs. It gives more updated stats than socialoomph. The graphs are available in a weekly, monthly or 3-monthly plot. Hourly and 6-monthly plots are available in a premium version (how much do we need them anyway?).
Useful for new twitter users, there's a profile checker that tells you what you need to do to having a good twitter profile so that you can increase your followers.
Although Klout is not just a twitter tool, it is worth mentioning here because of its importance. Klout scores are calculated as a cumulative of all the social profiles you add to it. The scores range from 1-100, the higher the score, the higher your sphere of influence. You can use other people's klout scores to identify influential people in your network. An analysis It is also useful to check out who your main influencers are and who are influenced by you.
Tweepi, Twitcleaner and Manageflitter
All these tools have the same essence -identify potentially 'dodgy' or inactive users for you, whom you can choose to unfollow. Tweepi and Manageflitter also identify active, 'talkative' and influential users in your lists. They also point out followers who you are following but are not following back.
Manageflitter goes a step ahead to recommend you a list of users who have been unfollowed by other users.
Twellow is a twitter directory, which lists 'tweeples' by their interests/tweets. For example, there are many categories including Bloggers, Doctors, Technology, London and so on, that helps you find new people by in a particular category that you can follow. This is a good way to find potential 'following'.
This was a brief overview of the popular and useful free twitter tools available in the market. Do let me know which ones you like and which good free tools I have missed out.