Games That Were So Good That You Played Them Again and Again.

I like to replay Victor Vran, Skyrim, the Van Helsing Series, DMC IV, the Darksiders series, and good platformers, like Ori, and the Giana Sisters, Shantae & and Rayman franchises.

Mine would be Metal Gear Rising: Revengeance. Story wasn't the best but the combat was really fun

Dota 2

Romance of the Three Kingdoms

Counter Strike

Freelancer, it never gets old!

Age of Empires and Spec-Ops: The Line

Planescape: Torment
Arcanum
Fallout 1-2
Star Wars: Knights of the Old Republic 1-2

A few come to mind
Fallout 3 / Fallout: New Vegas
Games so good, with such a great replay value. Sometimes I wanted to be a big guy in Power Armor and a sledgehammer, sometimes I wanted to be the sneaky-beaky sniper, sometimes I wanted to be the spawn of Satan and kill everything. Fun times.
Mass Effect trilogy
Just for the different stories and outcomes. Plus it's the first game I've actually felt stuff for the characters. Kudos to Bioware.
The Elder Scrolls Morrowind/Oblivion/Skyrim
Anyone who loved these games also replayed them for the same reasons as the Fallout series. Be who you want to be. Plus Morrowind will forever hold a spot in my heart for being the first game in which I got over 1000 hours (played it for 2-3 years when I was a kid).
The Witcher 3
I just can't let go of this world. It's just so good, words can't describe it. Will probably start my 4th walkthrough in the nearby future.
Gothic 1 and 2
Probably the first game I've ever played that allowed me to decide my own path. Joining different factions every time, using different weapons, so on. While the main story did not change based on decisions, it was fun to experiment with the different paths.
Star Wars: Knights of the Old Republic 1 and 2
Loved both games and would still replay them. Writing is so good, characters are so well made, I just couldn't play it JUST once, I had to replay it with different paths and decisions.

Other games I played at least twice, with the reason attached: Dying Light (fantastic gameplay), Portal (great dialogue and story), Metro 2033/Last Light (great atmosphere), Deus Ex: Human Revolution (great gameplay, worth a non-lethal approach), Bioshock Infinite (best escort quest ever), Spore (say what you will, I enjoyed that game when I was younger).

Sonic 1-3, Jazz Jackrabbit 1 & 2, Outrun, Streets of Rage, Super Street Fighter 2 Turbo, Mortal Kombat 3, Virtua Fighter 2, Tekken, Need For Speed 3 Hot Pursuit, Betrayal at Krondor, Betrayal in Antara, Might & Magic 6, Sacred, Heroes of Might & Magic 2 & 3, Broken Sword

Fahrenheit -- played it 4-5 times
L.A. Noire -- played it 3 times and will play it once more for sure
Max Payne 1-3 -- played each part more than once
Mafia II -- 3 playthroughs
The Elder Scrolls games, especially Morrowind
Also want to play Witcher 3 once more soon
+some "endless" games like Counter Strike and Binding of isaac

Prince of Persia : Warrior Within.
Played this game way too many times.
I still listen to its OST in my car.

Titian Quest: Immortal Throne, Diablo 1, 2, and 3, Torchlight 1 and 2, Elf Bowling, Defense Gride: The Awakening, and many more.

Arcanum x2 times :)

Plenty, way too many to list them all. Fallout 1 and 2, KOTOR 1 and 2 (even though I already beat both games on light and dark side), Zelda ocarina of time and majora mask, Mario 64, original Prince of Persia and Sands of time, Morrowind (beat twice, the third time I gave up), Arcanum, Max Payne 1 and 2, Dead Rising 2 (played 5 times, 3 of them with different friends), Saints Row 3 and 4 (same as DR2)....

After seeing the trailer of Shadow of War I am going to replay a little of mordor to see if i get the hype off my system. Even knowing the thing was scripted as fuck, its still cool.

Thought I'd bump this because I forgot to add in the GoG version of Sacred Gold. I keep that installed always.

I don't own the steam version.

Super Mario series
Donkey Kong series
Pokemon series