I found a great blog post on ProBlogger with many helpful suggestions on using Twitter effectively. I recommend reading it.
Additionally, I have a few tips of my own to improve your Twitter followers' experience.
DON'T use Twitter as a message board or mailing list. As stated in the ProBlogger post, if you converse back and forth with someone on Twitter, and someone is only following you, they only see half the conversation. Think about how annoying it is to hear half of a cellphone conversation. It's a weird and disjointed experience. Your followers may feel excluded and bored by your constant replies.
DO take your conversations to an more appropriate web asset. Move the talk to direct (private) replies, e-mail, or if it's a multi-person conversation, move it to a message board or mailing list. On a message board or mailing list,everyone can see the full discussion and join in.
DON'T use Twitter as a full-sized blog. Twitter promotes itself as a "micro-blog," where users can express themselves in 140 characters or less. It's usually acceptable to occasionally carry a thought over to a second Tweet.
DO use Twitter to link to your full-sized blog. If you would need to post three or more Tweets to express your concept or information, post all of it in one blog post or website paragraph and provide a quick description and link on your Twitter page. People will follow the link if they are interested.
DON'T allow spammers to follow you. Letting your follower numbers grow by not blocking (removing) spammers and deleted accounts is not only dishonest, it encourages spammers and other bad netizens to continue flooding the Internet with their porn, spyware, malware, and phishing programs.
DO follow people in your area of interest. If you are a gardener, you can search Twitter for other gardeners. Follow them and they may follow you. It's a good way to develop a network of like-minded individuals who can actually help each other.
DON'T be vulgar. I have stated this before, but it bears repeating since I see so many people damage their reputations by being sexually explicit, swearing a lot, and being mean, cruel, and sarcastic. Your boss or potential employer will seek information about you on the Internet. Even if your Twitter account is for personal use, demonstrating you cannot be civil and polite in a public forum will damage your chances for a promotion or job opportunity.
DO be positive and encouraging. It can be difficult in this instant reply world, but if you can't be nice to a fellow Tweeter, unfollow him (and block him if necessary). If someone Tweets some good news, send them (genuine) congratulations. If someone Tweets a concern or problem, show support and assist them. You have to give good to receive good.