I tend to play a small circle of games repeatedly rather than try everything once. This is mostly due to me not a rental place anywhere near by and being far too cheap to shell out cash for new titles. I buy and try some titles when I get them cheap and or used, with more and more titles of the current generation being play them once and then place them on the shelf.
As for games that I can play time and time again they typically fall into series releases. The playstation/2 Final Fantasys are frequent repeats of mine. 8 is in my top 5 list of all time games and 7, 9 and 10 are somewhere in the top 50. 12 I haven't played through as many times but thats because the first time I played my final clock was somewhere around 100 hours and I still hadn't done everything there was to do in the game.
Pokemon is another series I tend to play either continuous on the same save file or on occasion just a fresh restart. I enjoy the series mostly because I was about 10 when Red and Blue came out over here and I was ready to move on from something a bit more complex than the standard platformers and puzzles games I had been playing since preschool. Final Fantasy is a bit in the same boat here for when I began playing, as I first got my PS1 sometime in between FF7 and 8 and this being the time before everyone and their dogs were on the internet it was all still fresh and exciting to me. I then continue to play these because rather than trying everything that is new, I like to take comfort in the titles that are familiar and I know I will get a lerge chunk of gameplay out of. Don't get me wrong, I'm not pure retro only or a golden-age era fanatic, I just like a game that lasts a while and is fun.
Other frequent series repeats of mine that I can attribute to games I began playing around that age is the Zelda franchise. I love playing them and am never bothered by them being very similar to another in the franchise. The only beef I've had with the series lately was the controls on the Wii version of Twilight Princess, so I swapped it for the Gamecube version and loved every minute. Of course I have other games I play over and over, most of which are RPGs or the odd old platformer.
tl:dr version:
Zelda Series (mostly OoT, TP and WW)
Final Fantasy (mostly 7, 8 and 10)
Pokemon (usually play the most recent main series, but log well over 200 hours)
Tales of Symphonia
Golden Sun (1st one, didn't like sequel as much)
Mega Man 2 (only one in the series that I really really like)