You may know the situation: "ooh, a new game I want to play...but wait, I have an itch to play through this other game first." What games do you play through many times, even to the point of ignoring new games?

For me, in no particular order:
Super Mario Bros.
Super Mario Bros. 3
Super Mario World
Paper Mario
Paper Mario: The Thousand-Year Door
The core series Pokémon games (as evidenced by me buying the other version)
Minecraft (sort of, only when I find a good challenge map)

Games where I buy the next entry in the series to give myself an excuse to play through them again:
The third version of core series Pokémon
Animal Crossing

Games I've played through the story a million times and still play through them again on a semi-regular basis:
Paper Mario Thousand Year Door
Grand Theft Auto San Andreas
Grand Theft Auto IV + Episodes From Liberty City
Portal 2

Easy to pick-up-and-play often:
Any Mario Kart
Road Rash 64
Vigilante 8 + Vigilante 8 2nd Offense
Any Tetris

Original three Harry Potter games. Can't tell you how many times I've beaten Chamber of Secrets.

-All three games in the Mother series, usually with different challenges (No items, no PSI, get all the 1/128 chance items.) It's one of few RPGs I could replay over and over and never get tired of.

-Practically all Mario sidescrollers
-Classic Series Mega Man 1-6
-Sonic the Hedgehog 3 & Knuckles
-Sonic CD
-Super Paper Mario technically counts since I used and cleared all 4 save files
-Same with The Thousand Year Door
-SpongeBob Squarepants: Battle for Bikini Bottom
-Scott Pilgrim vs. The World The Game (and various other beat-em-ups)
-Cave Story (I've played and beaten all versions)
-Sonic Rivals 1 and 2
-Core Pokémon games I don't care about (All of 3rd Generation, Diamond, White)

-Dark Cloud 1 & 2 (starting to get over my hatred of 2)
-Crash Bandicoot 3 and Twinsanity
-The Jak and Daxter Series
-Ratchet: Deadlocked
-Sonic 3 and Knuckles
-Final Fantasy 10
-Ib
-Most of the Tales of series (Specifically Symphonia)
-Pokemon (The Main series of course)
-Kirby Superstar Ultra
-Mortal Kombat: Shaolin Monks (it's Co-Op is Awesome)
-Persona 3
-Mega Man X 1-5

Spyro (original 3 as well as first real 'reboot')
Okami
Sonic the Hedgehog (the ones for Sega Genesis)
The Legend of Zelda: Oracle of Ages/Seasons

Thaaaat's all I can think of off the top of my head ;'3

Jet Set Radio, Sonic Adventure, and for a while I replayed Antichamber over and over.

Any Mario game and Kid Icarus Uprising. Also Kirby's Adventure anda lot of other things xD

I've replayed every single Mass Effect game a minimum of ten times. I have twenty unique characters with complete playthroughs on the first game alone!

-Turok Evolution
-Alien Hominid
-Resident Evil 4
-Warioland 4
-Sonic Adventure 2 battle
-All pokemon game
-Any super mario game

Here are mine:

-Any Pokemon game upon urge
-Paper Mario series (except Sticker Star)
-Final Fantasy 9
-Super Mario Galaxies
-Bravely Default

I love my RPGs

I find myself replaying these a lot...

- Pokémon Ruby
- Pokémon LeafGreen
- Yoshi's Island GBA
- Sonic Heroes
- Pokémon Battle Revolution
- Super Mario Land

For me its:
Chrono Trigger DS
Chrono Cross (Have to get another one, lost mine)
Kingdom hearts series
Pokemon (Firered to SoulSilver only)
Pokemon Gamecube series
Yugioh series
Final Fantasy 7 (Same reason for ChronoCross)
Borderlands one (Just bought the DLC bundle)
Zelda series
Pacman 3ds
Mario series
Streets of Rage one
Sonic The Hedgehog: 1,2, & 3

I can keep going on for awhile.............

Oh my God, but how could I forget my arcade classics?

-Crystal Castles
-Donkey Kong
-Q*Bert
-Ms. Pac-Man
-Phozon
-Ninja Baseball Bat Man

And lastly but certainly the toppermost of the poppermost:
-DIG DUG! I play this all the time whenever I can and wipe my high scores so I can listen to that amazing music over and over...

An honorable mention is Baby Pac-Man which I would play nonstop if I were ever to find a machine.

Anyone ever tryed a game called Qix? I replay to see far i can get. (so far i can make to lv14)

I used to play the ratchet and clank games for ps2 religiously after beating it.

I wish I was able to go back to games I've played more often, but I have way too many games on a backlog...
-Super Mario Bros.
-Super Mario World
-Megaman 2
-Some CoD games(It's a bad habit, I know)
-Pokemon Ruby/Emerald/Leaf Green
-Most Namco arcade games
-Donkey Kong Country Returns
Not too many... :/

I always seem to drift back to is Sonic 3&K. It's such a good game to pick up and blow through, chaos emeralds or non.

For me I often replay games when I get hit by the nostalgia bug. The ones I recently got nostalgia-bombed over are:
Castlevania: Symphony of the Night
Legend of Dragoon
Tales of the Abyss
Super Metroid