If a game is made freely available with embedable code then they can be embedded anywhere, usualyl these games include adverts of some kind so although they appear free each play earns the creator money.
Alternatively they use the games to funnel people towards their bigger paid games. The websites themselves usually have their own rules, your best bet is to visit their site and look for their rules on the embedding of games.
Also its worth noting a website can monitor via their webhost cpanel who is embedding their games on the websites so they would be able to determine a site has taken their game and a site wouldnt therefore be able to rip the game off, also most embedded games are encrypted or use secure frames, so you might be able to make the game appear on your website but you wouldnt be able to steal the actual game itself.
Most browser based embeddable games dont make much money, so naturally people want as many people to play it as possible, the more sites embedding a game the more people that play it, this potentially can mean more money will be made, or will allow the developer to become more known for his game and therefore make more people take notice of future games he/she releases.