Maintaining healthy Twitter relationships takes a bit of work. In polite Twitter society, it is important that you spend the time performing upkeep on your social register of those you are following, since there are many people who may take offense if they follow you, and you do not follow them back. And we would certainly not want that.
Of course, one doesn't necessarily want to follow all one's followers. One is not keen to appear needy.
Unfortunately, keeping up with who's following you so you can decide whether to follow them back isn't easy on the Twitter site itself. Once you begin to build up a worthwhile group of followers, you'll need to turn dozens of pages on Twitter.com to manage your list. One has better things to do.
Here are a few tools that help you keep your social Twitter register up to snuff.
For the maintenance of balanced relationships
Twitter Karma: Give this tool your Twitter credentials, go get a cup of coffee, drink it, and then call your mother. When you're done, you'll have a nice page waiting for you of everyone in your Twitter network.
Next to each name, it will tell you your follower/followee status, so you can quickly see where the relationships are lopsided--where you follow people who don't reciprocate, and vice versa. Then you can click checkboxes to follow new people.
I didn't see a way to unfollow people from here, sadly. It is, though, very nice to be able to see your entire Twitter society on one page.
FriendorFollow: This tool performs a similar function to Twitter Karma, but it displays only the unbalanced relationships: people who follow you that you don't follow back, and those who follow you whom you don't follow.
It's good for giving you a picture of your Twitter politeness, but functionality is limited. It displays only user icons, not names, until you mouse over them, so reading the list for names is impossible without active mousing. Also, this tool doesn't let you actually turn on follows directly; it links you to Twitter.com for that. It's slow, but loading up the initial list is much faster than it is on Twitter Karma.
For those special personalities
TwitterSnooze: This is a useful tool for temporarily unfollowing a user. When people are Twitter-blabbing about a conference for a few days, and you don't give a whit about it, you can become blissfully unaware of their tweets for just the days that they are there. You can also use TwitterSnooze to just take a break from someone for a while.
Usually with Twitter, unfollowing someone is silent (but see below)--users will not get an alert when you stop watching them. But they do get an alert when you do refollow them, so with TwitterSnooze, they'll get new follow alerts when your snooze expires. That may lead to awkwardness among friends.
Qwitter: If you want to know if a particular person stops following you, use Qwitter (see Qwitter plays on insecurities).
If someone stops following you, it will tell with a pointed note, such as "John Gruber stopped following you on Twitter after you posted this tweet: 'What's the difference between Arial and Helvetica?'".
It's a great way to set yourself up to be hurt, though it takes some prep to get there: you have to specify the Twitter ID of each person you expect to offend you.
To keep up with those who matter the most
TweetDeck: This is yet another AIR-based Twitter client, but it has one very useful feature for the polite Twitter user: You can put a collection of people into a group and watch just what they are doing in their own pane. Even if you follow thousands of users, you could set up a group for just your closest friends, or just your nemeses, or what have you. It's a good tool for paying special attention to people.
Twitter Search: Search for your own Twitter ID. Grab the RSS feed for it. Subscribe to it in your favorite RSS reader. (Related: Monitter is three times better than Twitter's search.) Now you will know what the gossip is about you. Forewarned, my friend, is forearmed.