First thing is usually art and aesthetics because a screenshot (or packaging) is usually the first thing you see. "Graphics" aren't a huge deal to me but if it looks like they didn't put a lot of effort into the art then they probably didn't put a lot of effort into the entire game.
Next is a hook, either some kind of story or unique feature of the game. Something that when you hear/read you think 'hmm, that seems unique. I want to hear more'. This could be in the text description of the game or a video. I don't want to play a game that is a copy of others with nothing original. (unless it is a copy of a favorite game, I guess)
What really gets me hooked on games though is making me think, to put it simply. Someone mentioned Zelda games earlier, they are great with puzzles, strategy battle games such as Xcom and Final Fantasy Tactics, even first person shooters that aren't just run and gun but have stealth, cover, tactical vantage points, etc. Hitman was a favorite of mine due to having to monitor the guards and think what is the best way.
"Progress" is another good point. Leveling up in RPGs, getting better weapons in FPS, more money and bigger towns in games like SimCity type, Clash of Clans, etc. People feel good when they can see progress but I don't think it keeps people there if it gets repetitive.
Another important part is that it is challenging but fair. If it is too easy it gets dull from, well, basically not having to think. But it is frustrating if a game is 'unfair' such as you die or lose from no fault of your own, as in there was nothing you could do to stop it.
Hope this helps. As I'm becoming more comfortable with Construct I've been thinking more about what makes a game fun so I don't just make a game, but a fun game!