Freemium - Make the bulk of your game available for free, but provide paid premium content (e.g. Fantastic Contraption and Quake Live). There's obviously a bit of a balancing act with choosing how much to give away for free: you have to make sure you give enough so that they can enjoy the game, but not enough to satiate their appetite.
Adware - Make your game completely free, but with adverts. Ads could be in-game, around the game canvas (for browser games), or could be shown intermittently throughout the game (like television ads). Note that the viability of this is debatable (Quake Live was originally ad-based, but turned to freemium when they realised that they weren't making enough money to cover running costs).
Subscription based - Players pay a regular subscription fee to play (e.g. most MMORPGs). This could also be complemented with an initial free period (e.g. first month free).