Here's my criteria when looking for a new game...
Universal - I've got an iPad, iTouch and in a week or so an iPhone. I don't want to have to download a game twice.
No IAPs - or if you do have IAP's please make sure it's child protected!
Has it sold well on the App Store?
Does it have good reviews? iTunes reviews I don't always trust, I put more faith into peoples' impressions on forums like this one
Can I feel like I can accomplish something in a short amount of time (like 10 minutes)? I've found my favorite iOS games are the ones I can play in short bursts. Haven't been able to get into alot of longer games (RPGs, RTS, turn based, although I like these types of games on other devices)
I'm sort of a fan of over-the-top graphics and music in iOS games. By over-the-top I mean flashy, trippy visuals and techno-type music (or just music that gives off a good vibe (think Tiny Wings, Whale Trail, Sad Robot))
I keep coming back to a game if there's a high score to beat (personal or leaderboards), cool unlockables or if the gameplay is super addictive.
Usually if a game is only .99c and matches alot of the above criteria I will purchase with no remorse. I look at it this way, a cup of coffee costs more than .99c, but you get more pleasure/longevity out of a good iOS game