Honestly, I never have really thought of much about something like this. But let's see...
1. I want it, isn't that the #1 to anybody?
2. I almost always avoid RPGs and racing games, they're just not my thing. Maybe I should dodge puzzle games too, but only those with really complex puzzles, because I just can't do that. I normally go for shooters of any sort, but obviously I'm open to all the other genres out there.
2. DRM doesn't seem that big of a problem for me, obviously except for its absolute bullshit forms, but I prefer DRM-free games. I really don't mind Steam though. It has its problems, though, but I just don't mind using it.
3. I never have bothered to think about if it runs well on my computer, since it runs just about all the games I like, maybe some exception wherever, but I won't think too hard on that.
4. Price doesn't matter a whole lot, if I can afford it, sale or not, I'll probably buy it. I do despise the whole 60-dollar game thing though, I don't think many campaigns + multiplayers could ever possibly be worth that much.

Many people agree with you, myself included. ;-)

http://www.gog.com/en/wishlist/site/more_soundtracks_1

http://www.gog.com/en/wishlist/site/more_bonus_material_for_games_already_on_gog

Basic criteria:
1) No DRM

2) Gameplay is interesting

3) I like the story

Soundtracks are a good bonus.

• The game must be interesting enough to me that it strikes me as more appealing than any of the games currently sitting in my backlog (many, many things can contribute to this, so I won't try to get into details).
• Customer reviews must indicate that the game is relatively bug-free and gameplay does not include anything that I'd consider a major annoyance.

• If the first two conditions are met, then the game must be offered at a price commensurate with the value I place on it. For quality games that are DRM-free or that I can get a physical copy of with only a CD check I'll value them up to $50. If a game includes a one-time online activation then the maximum value I'll place on it drops to $20 or less. Any DRM beyond that (Steam, additional online checks, etc) drop the value I'll place on the game to $10 or less, and in particularly onerous cases the value will drop to $0, meaning I won't be buying it under any conditions.

This is pretty much exactly how I look at things, although my valuation of a client-required game (Steam, Origin, etc) is about 5 dollars. I may be tempted to slightly higher, but it's extremely rare. Other than that, spot on.

1. If it is possible to borrow from friends and families, try to borrow first :-P

2. If it is not possible to borrow but is still possible to rent from local game rental, try to rent first :-)

3. If I have to buy, make sure the game runs on my gaming rig first, for example by trying the game demos. If my machine cannot run it, do not buy it now unless I am absolutely positive I want to play it in the future

4. If I have to buy and the game runs on my machine, make sure it is DRM-free

5. If I have to buy the game and it is not DRM-free, at least ensure that internet connection is not necessary, or at least a no-cd patch or other crack is available

6. Always, always, always wait for sale and discount. If this cheapens intellectual property, so be it! You can't vote with your wallet when your wallet never holds much money to begin with anyway. Remember that gaming is my entertainment, not my job, and I do not run a charity organization for game developers either :-P

-No DRM, at all. CD check is as far as I'll go. If there's a chance that the game won't work 10 years after I got it for reasons other than hardware incompatibility (the client is down, internet is down, the registration site no longer works, the code I have doesn't work anymore because they changed their system, etc.), then screw it.

-Prolly will get flak for this, but no advertising that the game is indie. As far as I've seen, a game marketed as "indie" is typically an overglorified flash game that would fit comfortably in a site like Newgrounds. A good indie game doesn't need to rely on the buzzword: for example, I didn't even know that Psychonauts and Amnesia were indie until I heard they were in a recent humble indie bundle.

-Acceptable price. Depends on age and format of the game. On principle, a digital-format game should be cheaper than the hard-copy version. Otherwise, I'll wait for a sale.

-The game is such that the player has to become skilled at it in order to make it shine, like shoot-em-ups, fighters, etc. This means a well-thought-out scoring or combat system. If this doesn't apply, like in adventure games and (I would argue to a point) RPGs, then it should have atmosphere and an immersive story. Reviews explaining these types of details thoroughly are needed here.

-A solid single-player campaign, with high replay value either because there's multiple strategies to play through it, there's various mods available, or it's just that enjoyable to play. Multiplayer isn't that big a priority since I don't often have the opportunity to play with others, but if it's available then that's cool. Hopefully it would be at least decent. Again, reviews are needed.

That's all I can think of right now. I guess this is ordered by first general filtering, then getting to more specific details.

1) IS something I'd play/try.
2) Decent price
3) Can run on my machine (Which all of them should now)
4) DRM status
5) Retailer (GOG, Steam, etc)

It must get me interested enough I feel good about spending money on it (story, gameplay, location, characters,..).
I don't watch a lot of trailers nor prerelease photos so I don't receive spoilers, don't try demos. I do read a review in a magazine I trust.
One would think I bought many games I then did not liked, but one would be wrong. I have loads and haven't made a mistake yet in 15 years.
I also wait several months, even few years, so I can buy it at a cheaper price. I do prefer retail than DL, but I hate budget releases, only 1st release for me.

My general criterion is simple, really simple: if I like the cracked version of the game, I put it in my to-buy list. Well, except for that damn Diablo III thing....

- My interest in the game,
- Overall game quality,
- DRM [always online/rootkits/anal probes are a 'No buy']/Language version [i don't buy localized games],
- Price/Available funds.

There are certain factors that contribute but no one decisive factor.

- Positive word-of-mouth is always good for me, I pay little heed to mainstream reviews. It's how I got into Minecraft.
- Unusual or original game concepts are always of interest to me.
- DRM is usually an interest killer for me. Unless I really want the game, I will not buy the game at full price with DRM. I'm more inclined to take a chance on a full-price game I don't know if it has no DRM.
- I give priority to retail over digital. Digital for me is reserved for low-key indie titles, extremely rare and old games, or if the digital version is considerably cheaper than the retail version (i.e. €20 cheaper).
- The length of a game is not a deciding factor for me. I played Skyrim and loved every one of the 80 hours I spent playing it, I played Blood Stone and loved all six hours of it. So many games are so long yet so drawn out. Some of the best stories and gaming experienced are better served by a shorter game.

I personally find it a shame that the rise of DRM and digital on PC has made me more reluctant to take a risk on certain games, but hey, that's what my PS3 is there for.