First of all, if you ever want to archive your tweets before deleting them, it's easy.
Now that you've saved your tweets for posterity, you can start working on deleting your tweets.
To delete tweets with specific words, you'll want to visit Twitter Advanced Search.
If you want to try a free service for deleting batches of old tweets at a time, lots of people swear by TweetDelete.Net.
If you want a more serious service, you'll have to pay for it.
If it's good enough for The New York Times' Farhad Manjoo, it's probably good enough for you, too.
If you're on an iPhone, you can try Tweeticide. It costs $3, and it can similarly wipe out your 3,200 most recent tweets.
Android users have a nice option called Xpire, which — like the others — can delete up to 3,200 tweets.
If you really want to go nuclear, the only other surefire way to erase your tweets, aside from services like these, is to delete your account. Maybe it's time to start fresh, or leave Twitter entirely.
Twitter doesn't delete your account immediately; it holds your data for 30 days in case you change your mind.