Non-linearity - a big one. RPGs (with actual choices), Metroidvanias, open world games
Engaging gameplay and story/characters - Is doing the same thing once more still fun? Are the NPCs or party members worth encountering over again?
Atmosphere - Do you feel like you're just playing a game? Or, are you pulled into the environment being beamed into your eyes and replacing the player character with your own mind? Visuals, audio, and fluid controls can really help here.
Familiarity - If I really like a game, I probably will keep going back to it very often just because of the fact that I know it's good. My opinion of the state of the industry right now (don't like what's being made and don't trust much either) and finances also back up this point.
Art style or Graphics - Even if the game is linear, is the world fun to run around it and look at, time and time again?
Music - If the soundtrack fits the mood of the game, it will hook me even more.
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Metroid and Zelda are pretty replayable in my book. Exploration. Neat Gadgets to get to new spots. New paths to try in most of the titles. Their art styles are very gorgeous, even when they don't use cutting edge graphics. Zelda has tried many art styles that make them visually distinct and fresh. Most Metroids are dripping with the atmosphere of isolation - that you are alone and have to navigate a world of creatures out to kill without help. Metroid's music also adds loads to the mood of each area in each game.
I'm pretty sure I've played Guacamelee 6 times in the year or so I've owned it. (Maybe 7 hours for an average playthrough.) It is that good. Lot's of colorful art inspired by Dias del los Muertos. Addicting luchador fighting. The characters are pretty engaging for a game about pile-driving skeleton warriors, and humor is in almost every cutscene. The look and musical themes are amazing.
Some of the old Final Fantasies have more than one playthrough from me. (4, 6, 7, 9, 10, 12) IX probably has the best story out of the franchise, and there is a lot to do beside grinding in all of those games (except maybe 4). Uematsu's soundtracks are also gold.
I also fall back on 90's Crash, Spyro, and Sonic. Nostalgia of course comes into play, but they did what they sent out to do well. It's still fun to run around jumping on robots/fierce creatures and collect shiny things.
Classic Doom is, well, Doom. Do I need to mention why I love firing up these every time I feel like fighting something with huge guts using the great communicator?
I also like going back to the original Halo. It had the right amount of mystery around the villains, the hero, and the setting. The pacing and most of the weapon balance was better than latter games. The latter half's backtracking through old levels is seen as cheap by some, but I find it to make the game seem like the Chief is really traveling around a connected world, not being teleported (even though that's what happens in-story) like in some FPSes and othe genres.