The main things I look for, in order;
-Replay Value
--If I can beat a game in less then twelve hours non-stop, back to the store it goes!
---There are some exceptions to this, but I don't feel like explaining them.
-Story Line
--If a game's story grabs my attention, BIG plus there!
---If it is shit, I stop playing right then.
-Gameplay
--Being a hardcore RTS player, RTS games own, I don't care if the graphics are the worst ever and the story is pure bile, I'll still play the damn game!
---For FPS/TPS and RPGs, my standards are a lot higher.
-Graphics
--Graphics can be a major plus if done right. Back in the day, StarCraft's cinematic movie graphics were TOP of the line, and it was more of them that got me hooked on SC then the other stuff.
---Games like GTA, they should be much better, but you can't expect much from RockStar Games now can you?
In any event, I'll play just about any game at least once all the way through. If I like it, I'll keep playing it, if I don't like it, I uninstall that thing fast and move on to the next game(or fall back on a SC).