I have been playing Crazy Taxi on and off for twenty years. Just like any good arcade style game, it keeps me coming back. Also just like any good arcade game, I've never really mastered it. Sega always excelled at arcade games, and Crazy Taxi is one of the best of the lot. It first came home to the Dreamcast console. Given that I had a Dreamcast at the time, Crazy Taxi was an obvious purchase for me, and is still my preferred version of the game.
When it comes to genres, Crazy Taxi’s is hard to nail down. I wouldn’t really call it a racing game, but you are driving a car. You're a cabbie, and your goal is to pick up passengers, and drop them off as quick as you can, by any means possible. Your are timed, and when time runs out, the game is over. In addition, each passenger has a set time limit for getting them to their destination. You can earn more overall time by getting them to their destination faster than the limit. So the gameplay is a constant cycle of picking up a passenger, driving them to their destination, usually causing mayhem along the way, dropping them off, looking for a new passenger, and repeat. Wikipedia calls it a “score attack racing game”, which I suppose is fair enough.