There are several
computer games that I can think of that the player is supposed to be evil:
The Dungeon Keeper series has the player capturing heroes and torturing them as either entertainment or to convert them to your cause. Can't say I've gotten around to playing this one yet, though.
Black & White is half real-time strategy and digital pet simulator. Albeit your pet is a huge bipedal animal and humans are but tiny insects in comparison. But there is the potential to be an evil god and therefore have an evil animal avatar. The look of your pet, your temple and evil the land inside your influence reflects how good or evil you play.
Grand Theft Auto series has you playing a car thief, hit man, drug runner, and gang member, if you so please. In fact, stealing cars and/or murdering their former owners is par for the course. There are very few redeeming moral actions, besides saving one of your own cartel members.
One of the No One Lives Forever games has you playing as a member of H.A.R.M.. Can't say I've played this one either, but it's true. It's not a very long game, more of an expansion pack, from what I've heard.
The Aliens Versus Predator series casts the player in the role of the Predator, Alien, or Marine. Obvious, the human is the 'good' character and doesn't have do anything immoral, just survive. The Predator and Alien are debatable evil characters, since the each do only as their biology suggests. In the case of AvP2, the Predator has an even worse human nemesis to go after. Any Marines that get in the way are incidental. Aliens are mindless killing machines in own right and have few objectives. Kill, reproduce, and protect the Hive. So, barring a discussion of morality, the Predator and Alien characters are evil in that they kill human beings for sport and food, respectively. They only look out for their own species.
The two Postal games cast the player as a psychopath mass murderer. Go figure. The first game had wonderfully painted backgrounds, but the gameplay and the horror quickly became repeditive. The second game, however, despite being entirely politically incorrect, had many original ideas and conform to very few of the above cliches. So you're on fire? Pee on yourself. Want more health than you would normally? Smoke some crack. The player just wants to finish his seemingly mundane tasks (get milk, go to the bank) but the game world goes out of its way to goad the player into reacting violently. Sure, you're killing innocents, but they were annoying to begin with. It's probably the only game series that puts the company that produced the game into the game itself as a plot device. It's certainly not my favorite game, but it does things (albeit in a very offensive manner) in an original and never-before-seen fashion.