Online Casinos are fairer than many people realize. The "house" is happy making the normal profits of gambling. In many of the countries, the computer programs must be submitted to the government for thourough checking of fairness toward the player, and the firm also has to be guaranteed by one of the big eight international accounting firms.
In all cases with casino gambling the odds for single deck blackjack, for instance, are exactly the same with an Internet casino as with the real thing. The same is true for baccarat, roulette etc.
As for the gaming machine type games (slots, video poker etc) the player payout percentages are determined by the casino, and many will post what the percentage of payout is online.
There are lots of great places to play online poker and here is a list of links to reviews of the best poker rooms: