The biggest problem I have with games in general is how a game "handles." There's two parts to this equation:
* Ability to remap controls. If I don't like how the default controls are laid out, I should be allowed to remap them. This isn't usually a problem in most of the games I play, but in games like Scott Pilgrim vs. The World, I should be allowed to at least remap the Block button to the triggers instead of being forced to use a face button. :V
* Freedom of movement. I like characters who can move and attack at the same time, or at least not feel locked into place for too long when I need to get out of the way fast. Bayonetta does this well, and even Hyrule Warriors feels very fluid and swift with running around (getting around the battlefield is important, after all). Sadly, an example of how not to do movement well is in a game I had an interest in playing: Copy Kitty. It's pretty much touted as a Run and Gun, but the way the main character handles is counterproductive to that. You can't run left or right while shooting, and the only way to move while shooting is to jump. I'm sure if I practiced enough I'd get over this limitation, but it seems more of a hassle than it's worth. A shame, too: Copy Kitty is an interesting game and I'm sure I'd enjoy it more if the character wasn't so limited.
tl;dr Control makes or breaks a game for me.