Many of us would have played 20 questions at some point of time or the other (a game in which a person thought of some object/famous person & another person had to guess by asking a maximum of 20 questions, with answers being monosyllabic in nature). I liked to play it quite a lot. However you require two players for the game.
Now though, it is possible to play it online against the computer at the following site: 20q.net (actually it has been around for a while). The computer is usually quite good at guessing the object you thought of, though it might at times ask irrelevant questions. It can also learn new objects not in its database. Also if you try to mislead the computer by giving wrong answers, it will point out contradictions when you give out the answer finally or when it guesses correctly.
There was also another flash based site (sithsense created for Burger King) which used the 20Q engine, but with a radically different UI. You had Darth Vader (from the Star Wars movies) asking you the questions. The original 20Q site seemed to be better at guessing though, but this ones probably more fun to play. The site seems to have been archived & asks for authentication now. The authentication information can be found here (cpbgroup site).