This question is worded a little ambiguously, perhaps intentionally... what does "support" mean? I certainly support the development of new games, by which I mean that I always want people to try to make games.
As for financially supporting unfinished games, sometimes I do and sometimes I don't. I've been refining my criteria (see below), but it depends on the situation. I have not supported any game projects on Kickstarter, however I have purchased about a half dozen Steam Early Access games. I have also "bought into beta" a few times too (ArcheAge and Landmark are the biggest examples).
To me it all boils down to risk versus reward.
Kickstarter is a fairly high risk, low reward proposition in my mind, so it doesn't make much sense to back a game project there unless you happen to know and like the developers. The risk is that the developer will take your money and run, or never finish the game, or change the game entirely from their initial proposal. The "reward" is a lot of buggy releases, and a few dollars off the eventual retail price. (Increasingly I'm also wondering if people consider it a reward to have the opportunity to psychologically terrorize a developer on their early access forums.)
Steam Early Access is more of a low-to-medium risk, with a higher reward (mostly instant gratification). There are a lot of reviews there you can read to help you decide whether or not to take that chance. And if you wait a few days after the game "launches," you can almost always find someone who is streaming it so you can actually look at it first, or bloggers will write up some first impressions of it.
Buying betas (or "founder's packs") is more of a case-by-case basis. With ArcheAge and Landmark, I considered them extremely low risks, with decent-sized rewards. I knew I would like ArcheAge because I'd already played the Russian version, and I was pretty excited to play the Westernized version. True, I paid a premium to play it early, but considering the value of the virtual goods in the founder's packages, it wasn't that much of a premium.
As for Landmark, I didn't know anything about the game, but I trusted (and still mostly trust) that a company like then-SOE-now-Daybreak will actually finish the game and get it to market. So I knew I wouldn't lose my money. But in retrospect, I probably should have waited. I don't exactly regret buying a founder's pack, but if I had known the condition of the game before making my purchase, I would have waited. Because they were basically selling us a prototype.
And because of that Landmark experience, I've set myself some loose guidelines on how much I will spend on unfinished games.
If it's a totally unknown game from a totally unknown developer, I won't spend more than $10-$15. This also includes games I might be interested in but have seen or heard lukewarm reviews, or seen game footage that makes me wonder about the quality of the developer studio. I have a lot of Steam Early Access games in my wish list in this category. I won't buy them unless they go on sale.
If it's an unknown game but I trust the company, or I like what I've seen in game footage or streams, or it's getting good reviews from peers, I might spend $20-$25 on early access.
(If it's a known game but the publisher is Daybreak, who is known to release prototypes as products, I won't buy it unless it goes on sale for much less than $20. That means H1Z1.)
These days I can't see myself spending more than $25 for an unfinished game unless it's backed by a major AAA studio, or at the very least has a free demo that I can try first. Unless a game concept just blows me away, I can wait until the open beta or the release date. I've got plenty of other games to play and not enough time to play them as it is.
But I'll always reserve the right to change my mind and buy something on impulse.