Sigh. I don't understand people who say things like "fun" in response to questions like this. If someone asks you what kind of food your like, or what your favorite food is, it is not a legitimate answer to say "the delicious kind."

The question actually being asked is obviously "what do you find fun in games?" Denmark is the only person who has legitimately answered this question, I think. Karifean arguably has with the first half of the answer.

Anyway, I look for one of the following: Immersion (which is hard to find), depth of strategy and progression (somewhat easier to find), or accessibility of the game to being played without thought, skill, or practice.

The first kind of game is something like Skyrim (which is a mediocre game maybe a 6.5/10, but a good example in what it's trying to accomplish and is well known).

The second type would be a game like X-COM, or King's Bounty, or the Total War series.

The third type is something like Mario Kart or Dynasty Warriors.