For 20 years I've kept a handwritten journal of books I read and now I also keep the list online at Goodreads. You can see a screen shot of the titles I've recently read to the right.
Goodreads is a social media site where booklovers can become online friends, share book reviews and recommendations, join genre groups, take literary trivia quizzes and generally spend time online goofing off but feeling slightly superior because it's all about books, isn't it? Goodreads is free to anyone to use. My children joined it and invited me to join and "friend" them so we can see each other's reading lists and share our thoughts on what we've read. I know, it's all rather futuristic, like something the Jetsons might have done, but it works for us.
BHPL subscribes to a similar service called The Next Good Book which is linked to the library home page. Ellen discussed it on the blog here.
For a really low-technology way of keeping track of books you read, save your library checkout receipts and throw them in a shoebox.