Would you pay for a game that doesn't exist yet? That sounds a bit like a crazy idea, but in fact the possibility exists in various forms. For example I already paid $5 for my pre-order of Star Wars: The Old Republic. I'll get the money back when I purchase the game, but right now I'm out of pocket $5 and have to hope that the game actually releases, or if not that EA would refund me my pre-order. EA being a big company and SWTOR such a big project, the risk of the game and my money disappearing is minimal. But there are other examples with more risk.
One other game I paid for which isn't released yet is Glitch. I'm in the beta, I like the game, and they had an offer where whatever you pay now for subscription advantages is applied to both the beta and the release version of the game, so it is kind of a full-price pre-order. The risk is obviously higher, but Glitch is a game I believe in, and which I am happy to support in the beta stage.
And then there is Kickstarter, a website on which you can fund various projects which only exist in an early planning stage. For example you can give money to fund the NASA MMORPG Astronaut: Moon, Mars & Beyond. 645 people did so, giving a total of over $33,000. Every project has a list of rewards what you'll receive if you pledge money to that project. The more you give, the more you get, so a small donation gives you beta access, a big donation gets you an appearance as 3D hologram in the game.
If you aren't interested in the moon, you could also give money to the Steampunk MMORPG Notch. They only got 59 backers up to now for under $3,000. Again there are rewards for pledges depending on how much money you give them, ranging from beta access to having a god named after you. More info on Notch here.
While interesting as a concept, the risks of funding a game via Kickstarter are obviously high. You are giving money to people you don't know based on a video and some concept art. If the game fails to ever be released, your money is gone. And even if the game is released and you get your reward, you can't be sure that the game is really that great as advertised. But if you really believe in a game, Kickstarter is a way to put your money where your mouth is, and maybe get in at the ground floor, scoring some unique rewards that won't be available any more later in the development cycle.