For me I prefer games with either a strong story in the one title, or entries that make up an entire series with a great plot.
So for me, Bioshock 1 and 2 (the plot and world are so fantastic it drags you back), Borderlands 1 and 2 (I just love the wackiness and insanity paired with the challenging difficulty), the Devil May Cry series (you can't hate on Dante no matter how hard you try), Dragon Age: Origins (and 2, to an extent) because of the amazing plot and great world, some Final Fantasy titles (X was my favorite), the Gears of War trilogy (because despite everyone's constant mocking, it actually had a solid plot behind all the gore-tastic gameplay), the Halo series of course (except for Reach. Worst entry ever), the Jak and Daxter series (the world is outlandish, as are the weapons and enemies), the Kingdom Hearts series (my personal favorite, I've played/beaten them all multiple times), the Mass Effect series (I can replay them endlessly, 3's ending really didn't bug me), Persona 3, 4, and Arena (they're incredibly solid JRPGs that balance out light and dark elements to weave a fantastic tale), the Ratchet and Clank series (my other personal favorite, the variety of guns mixed with the fantastic combat just makes it endlessly addicting), Star Wars: Republic Commando and the two Force Unleashed games (because they're brilliant story entries) (I'm not posting KoTOR or KoTOR2 because I haven't beaten them yet), and two Tales of games, Tales of Symphonia and Tales of Vesperia (they're both equally brilliant)
Yes, long post, lots of titles, bit I have a lot of games to choose from.