You can sign up for a free account here - ManageFlitter.com. This has both a free and a for-pay aspect to it. Like most of these systems, you get a curtailed list of options until you pay for the full account.
Unfollow the Dead Weight
ManageFlitter lets you look through the people you are following and see if some of those accounts just aren't worth it any more. Every person you follow is precious, since you have a limit based on how many people are following you. You want to make sure you're following as many genre-matching people as you possibly can to build those relationships and retweet valuable information. So you can sort the "people not following you back" by their latest tweet time, the number of followers they have, and so on.
You can see in this screenshot that I have people I'm following who last posted in 2011. I probably followed them back then and forgot all about them. It's time to remove them from my list.
Why did these people stop posting? Who knows. Maybe they lost their password and just made a new account. Maybe they changed interests in this topic. Whatever the reason, if they're no longer active, there's no reason for you to follow them any more. Let them go and use that space for someone active.
I like this display. It shows you the latest post and other information so you can make your decision quickly and easily.
Managing Followers - Ooops
Unfortunately, you can't even manage followers at all without paying them money.
You have to pay either $12/mo or $49/mo to get access to those advanced features that most other tools give to you for free. And, again, this is PER ACCOUNT. So if you have multiple accounts this adds up quickly.
If they gave you even basic follower maintenance options for free I could recommend it. But the way their free system is set up, you get far less than the many other options that exist out there.
Building Traffic for your Twitter Account
Followers and Twitter's Value
What is a Twitter Hashtag?
Maintaining Multiple Twitter Accounts
Choosing a Twitter Icon
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What is a Twitter Hashtag?
Twitter for Authors
Twitter Promotion Tips
Twitter Next Step
Twitter 2000 Follower Limit
TweetDeck - Free App for Twitter
TrueTwit - Prevent Twitter Spam
Tweepi - Manage your Followers
ManageFlitter - Follow and Unfollow
FollowerFilter - Great Free Follower Management Tools
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Twitter Business and Pleasure by Erwin Calamer
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