You can beat almost any game.
The most recognizable are poker, sports, horses, blackjack and video poker.
You would need to use a complex count or find a game with perfect rules to eek out a small edge. Basic strategy will not beat BJ. Try the game in downtown LV at the Las Vegas CLub. They deal a game where you can double down on three or four cards , get paid for 5 cards under 21 (auto win), can split AND PLAY aces, and I think a few more rule changes. The limits are lower (maybe $200).
Video Poker is doable on the right mnachine, but it requires perfect decisions. I think one mistake an hour can cost your the edge.
Poker is obvious since you play against other saps. It is hard to beat sports and horses over the long term, but people certainly do it.
Slots CAN be beaten, but only in special situations, like the ones Strut mentions. You would have to take advanteg of special promotions, or bonus banks. For example, technically, when a jackpot reaches a certain percentage, it could be statistically vaible to play. I would never personally do it though.
As for craps, roulette, and baccarat, no matter what anyone tells you, these games can not be beaten. The only way would be to cheat, factor in your comps, or take advantage of special rule promotions (Bonus Bets, etc.).