I'm going to distill it down to just one major element. Although the experience as a whole that is created by every element of a game coming together is essentially what's going to make the game good or great, I'm going to throw the inclusion of meaningful choices out there as the most important single aspect for me.

Now meaningful choice can take any number of forms. It could be as simple as choosing between different routes in a single player FPS (and yes, despite their modern linearity they still have multiple paths through sections much of the time, at least in the good ones), deciding which class to play to most help your team in TF2, which spells to teach a character or party composition in an RPG, or whether you're going to rush or expand, or when to scout and what to do with the info you get from it in Starcraft. The choices don't even necessarily have to be something that you sit and ponder over like you'd find in dialog options in games like Fallout 3 or Mass Effect. They can be fast and require split second decision making, just as long as they have the potential to dramatically affect what happens in the game and your experience playing through it.

There are other factors that can come into play as well, often working in concert with choices though, like the challenge level of the game. Choices become less meaningful if there's less challenge because the consequences of choosing one thing over another are lessened.

Now this isn't to say that graphics, art style, sound, music, story, and characters aren't important but without the ability to make meaningful choices I not only feel less engaged and immersed because I feel interaction is key to immersion, but I start to feel like I might as well be watching a movie instead of playing a game.