Personally, the way to hook me in game is good game mechanics. I don't care if you have a good story or whatever but if there's almost non-existent game mechanics in the game, I would get bored easily. But, there's still a way for me to enjoy them which is if I watch Let's Players play them.

Graphics should feel polished, smooth and detailed but not so gritty that you can't see the important items.
Good: Quake 3 Arena had the perfect balance between smooth curves and detailed scenes.
Bad: Shadow Warrior 2 has way too many details. Cramming in more stuff than the player can perceive is just annoyingly distracting.
Terrible: Games with random store assets are ugly as hell because they all converge towards the cheapest style possible using fast mud sculpting and baked light instead of taking the time to design quality textures. Even if you're not a good designer, a simple unique style made by the same person is way better than random models made by different professionals.

Controls should be easy to get started with and feel intuitive, but tactics should have depth.
Good: Prince of persia sands of time had a special edition that came with a controller for the game. Easy controls to remember, yet advanced puzzles and climbing.
Terrible: STALKER Shadow of chernobyl had too many complex menus that distracted from the game while the game itself was mostly empty forests where you would bleed to death no matter what you did.

Randomness makes a game more interesting by not being able to solve the level in the same way next time.
Good: Alpha Centauri makes each match feel unique by randomizing most things.
Bad: Project IGI 2 has no randomness at all, so finishing a level is often steered into a learned combination of key presses even if you try to be original. It could otherwise be a good game if it had some surprise.

Story has to go well together with the gameplay so that it's not like watching random scenes from an unrelated movie.
Good: Deus Ex tells the story without overusing cutscenes.
Bad: Max Payne 3 is super powered in gameplay, yet he's a drunk who can hardly walk in scenes where children steal his gun.

Real-time strategy games are (in my opinion) the best games (like Warcraft III, Age of Empires and Stacraft).