The World Ends With You 3 times (DS)
Phantom Breaker Battlegrounds 8 times (PC)
Dark Souls 4 times (no dlc)(PC)

Edit : corrected Dark Souls, skipped some covenant spells and weapons, so not 100%.

Dark Souls (PS3) 8 times & 100%
Dark Souls II (PS3) 5 times & 100%
Crash Bandicoot 3 (PSX) 6 times (PS3) 3 times (Vita) 1 time 100%
Crash Team Racing (PSX) 2 times (PS3) 1 time 100%
Crash: The Wrath of Cortex (PS2) 8 times 100%
Crash Tag Team Racing (PS2) 3 times 100%
Ratchet & Clank 3 (PS2) 9 times 100%
Uncharted 3 (PS3) 4 times 100%
Uncharted 2 (PS3) 4 times 100%
Rayman 2: The Great Escape (PSX) 2 times (PS3) 1 time 100%


Kudos Teeqoz for beating Ratchet & Clank 2 12 times! I've beaten it only 4 times because I enjoyed Ratchet & Clank 3 much more than Ratchet & Clank 2. ^^ 

I've played Witcher 2 to completion 5 times on PC. I'm pretty sure that's more than any other game i've ever played.

Souls are up there, but someone has no doubt beat me.

(PC)Age of Empires 2 - x 2*100% campaign. also x2 *100%for the AoE2 Conquerors expansion. 
(DS) Dragon Quest 9 - x3 and a half
3DS Super Mario 3D Land - x2*100%
3ds Samurai Warriors Chronicles x 2

I plan to do Bayonetta's twice later in gen but that's all I can 100% remember.

I usually replay games which made up my childhood every ounce in a while, so don't laugh at this....emm..childish selection of games. I also some reply most games on another platform so as to get a new experiance:

Toy Story 2 (PS,PC): 4 Times
Ben 10: Ultimate Destruction (PS2,PSP): 2 Times
Toy Story 3 (PS2,PC,PSP): 4 Times
Spider Man 2 (PS2, PSP): 2 Times

Am currently replaying:
Ben 10 Alien Force: Vilgax attacks (PS2,PSP): Finished 1 play, just started the next.
Secret Sturdays: Beasts of the fifth sun (PS2,PSP): Finished 1 play, half way through the next

I don't replay that many games lol . 

I like this. My acconplishments:

Super Mario 64DS (DS). Beaten 3 times, 100% once.
Pokemon Ranger (DS). Beaten twice, 100% once (on going second 100% run)
Pokemon Soul Silver (DS). Beaten 4 times, failed 1 Nuzlocke run.
DBZ: Budokai Tenkaichi 2 (PS2). Finished 3 times.
GTA: San Andreas (PS2) and GTA: Liberty City (PS2). Both finished 2 times.
Pokemon X (3DS). Finished once, failed one Nuzlocke challenge (not sure if this counts)
ToZ: Skyward Sword (Wii). Finished 3 times, once 100%, 6 heart run once. Next attempt: Hero mode, no shield, 6 heart run.
ToZ: Ocarina of Time (3DS). Finished twice. 100% once.
ToZ: Phantom Hourglass (3DS). Finished twice.
Super Mario 3D Land (3DS). Finished twice. 100% once.
Super Mario Galaxy 2 (Wii). Finished twice, 100% once.
New Super Mario Bro. DS (DS). Not very sure, but let's say 3 times. And if that's the case, 100% twice.
VVVVV (3DS). Finished twice.
Pikmin 3 (Wii U). Finished 2 times. 100% once. Just started my 3rd run.

That should be it. I would put more Pokemon games, but mostly are failed nuzlockes or different versions, which I don't know if those count.

Some games, like the Mario series and fighting games, I have finished way too many times to know the exact count, so I won't include them
The numbers I'm mentioning here are number of times I know for sure I've done. But they may be higher than that. Trying to remember properly over 25 years of gaming is kinda hard. xD

 SNES and Virtual Console

- Final Fantasy IV - I stopped counting at 21 times *
- Final Fantasy VI - I stopped counting at 10 times *
- The Legend of Zelda - A Link to the Past - 8 times  *
- Super Metroid - 20 times *
- Chrono Trigger - 7 times 
- Secret of Mana - 4 times 
- Flashback - 2 times 

Playstation

- Final Fantasy VII - 6 times *
- Final Fantasy VIII - 4 times *
- Final Fantasy IX - 4 times *
- Final Fantasy XII - 3 times *
- Metal Gear Solid - 10 times *
- Chrono Cross - 3 time
- Suikoden - 3 times 
- Suikoden 2 - 2 times
- Lunar The Silver Star Story Complete - 3 times *
- Legend of Mana - 3 times
- Castlevania - Symphony of the Night - 5 times

Dreamcast

- Shenmue - 4 times
- Skies of Arcadia - 2 times
- Resident Evil - Code: Veronica - 4 times
- Legacy of Kain - Soul Reaver - 2 times

PS2

- Dragon Quest VIII - 4 times *
- Metal Gear Solid 3: Subsistance - 3 times

Gamecube

- The Legend of Zelda - Wind Waker  - 4 times *
- Paper Mario - The Thousand-Year Door - 2 times
- Luigi's Mansion - 3 times
- Metroid Prime - 5 times *
- Metroid Prime 2 - Echoes - 3 times *
- Metal Gear Solid - The Twin Snakes - 2 times
- The Legend of Zelda - Twilight Princess - 3 times *
- Resident Evil - 3 times 
- Resident Evil 4 - 4 times

XBox

- Shenmue 2 - 2 times

XBox 360

- Fable 2 - 3 times
- Lost Odyssey - 3 times
- Grand Theft Auto IV - 2 times
- Bioshock - 2 times
- Mass Effect - 2 times

Wii

- Super Mario Galaxy - 3 times *
- The Legend of Zelda - Skyward Sword - 2 times *
- Metroid Other M - 2 times *
- The Last Story - 2 times 

PS3

- Metal Gear Solid 4 - Guns of the Patriots - 4 times
- Uncharted Drake's Fortune - 5 times
- Uncharted 2 Among Thieves - 12 times *
- Batman Arkham Asylum - 3 times
- Uncharted 3 Drake's Deception - 3 times
- The Last of Us - 4 times
- Prince of Persia - 2 times
- Flower - 5 times
- God of War III - 3 times
- Heavy Rain - 4 times
- Red Dead Redemption - 2 times
- Final Fantasy XIII - 2 times

PC

- Maniac Manstion - 15 times
- Days of the Tentacle - 5 times
- Warcraft: Orcs & Humans - 2 times
- Warcraft II: Tides of Darkness - 6 times
- Warcraft III: Reign of Chaos - 2 times
- Fable 3 - 2 times
- Deus Ex - Human Revolution - 2 times
- Batman - Arkham City - 3 times 
- Sleeping Dogs - 2 times
- The Witcher 2 - 2 times
- Dust: An Elysian Tail - 2 times
- Skyrim - 2 times
- Bioshock Infinite - 3 times - PC
- Tomb Raider (reboot) - 2 times
- Resident Evil HD Remaster - 2 times
- Ori and the Blind Forest - 8 times 

Wii U

- The Legend of Zelda - Wind Waker HD - 2 times *

I'm leaving quite a lot of games and consoles out... But it took me a while to make that list and I kinda got tired of doing it. xD

ive beat the last of us 11 times now :P spread across both gen ofcourse, so not sure how you wanna count that. (8 on ps3, 3 on ps4)

Ooh, forgot Metroid Zero Mission (GBA)! 4 times, never 100%

Does Star Fox 64 (3DS) count? You finish the main campaign in 20 minutes :-/

Games completed 5 times or more

F-zero GX - 30 times (gc) won all five grand prix's on master with every one of the 30 racers.
Silent hill- 20 times ( ps2 x4, xb360 x8, ps3 x8) you had to complete it 8 times on ps360 to get all achievements.
Resident evil 4 - 18 times ( gc x15, ps2 x1, xb30 x1, ps3 x1)
Metroid prime - 15 times (gc)
Silent hill 3 - 12 times (ps2 x4, xb360 x4, ps3 x4)
Ocarina of time - 8 times (n64 x5, 3ds x3)
Twilight princess - 7 times ( gc x3, wii x4)
Wind waker - 7 times (gc x5, wii u x2)
Super mario sunshine - 6 times (gc)
Final fantasy X - 6 times ( ps2 x5, ps3 x1)
Metroid prime 2 echoes - 6 times (gc)
Super mario galaxy - 5 times (wii)
Metroid prime 3 corruption - 5 times (wii)
Uncharted - 5 times (ps3)
Skyward sword - 5 times (wii)                                                                                                                                                                                    Bioshock - 5 times (xb360 x3, ps3 x2)