Can you count cards at baccarat? Yes. It works partially in a similar manner to blackjack -- cards are dealt from the shoe and the shoe is not usually shuffled after each hand, so there are dependant trials in baccarat, which means that what happened in the previous hand influences your chances of winning in the next hand (unless the shoe has been shuffled).
Unlike in blackjack games, though, card counting at baccarat is possible in theory, but you won't be able to make a significant profit.
Famous gambling authors like Peter Griffin and Edward O. Thorp have proved that counting cards at baccarat wouldn't be worth the time even for computers (which count perfectly without mistakes).
As the Wizard of Odds proves, the money you could make by counting cards at baccarat is extremely minimal and you would have to bet only once in every 475 hands - that's neither fun nor profitable enough (think of how long you'd have to wait around for 475 hands of baccarat to be played).
You need to get lucky in order to make money at baccarat. It's a fine, entertaining game though with a house edge of 1.17% for the best bet so it's certainly a cheaper form of gambling that slots or roulette, but you can do better at blackjack. In my opinion, blackjack is a better game considering both house edge and entertainment.