There are a number of reasons why you might want to delete your Twitter account. Maybe you just don't use it. Maybe you can't stand another hashtag. Maybe you said something stupid and have half the Internet mad at you ("Come on, it was only satire!"). Whatever the reason, nuking your Twitter account is an easy process that only takes a few mouse clicks.
To start, visit Twitter.com and log in to your account. Once logged in, locate the settings menu--represented by a gear icon--and select it. Next, select Settings from the menu, and on the resulting page, scroll to the bottom and select Deactivate my account. Twitter will ask you to confirm that you really want to deactivate your account. If you do, click the Deactivate button, and don't ever return to Twitter again.
What exactly does this do? Twitter will remove your profile and tweets from the site, and if someone tries to view your profile page, they'll get a message saying that your account doesn't exist. The company warns that "some content may be viewable...for a few days after deactivation." Also, tweets and other content you posted to Twitter might still show up in search engines. As they say: you can't ever really remove anything from the Internet.
If you feel remorseful after nuking your account, though, you have 30 days to change your mind: Twitter will retain your account and user data for that period, and all you need to do to reactivate your account is to visit Twitter.com and log in with your username and password.