I'm not sure how to handle NG+ runs as my experience is you can run through an easily 30-40 hours game in as little as three or four hours since you don't have to go off the beaten path at all having done most of what the game offers in the original run. For the purpose of my listing I'm going to make a separate NG+ rank. 

1. Metal Gear solid 2 @ 30+ completions

2. Metal Gear Solid @ 24+ completions

3. GTA 5 @ 5 completions

4. The Witcher 3 @ 3 completions

5. Divinity OS @ 3 completions

New game modes currently sitting somewhere in...

1. Sekiro NG+ 6

2. Bloodborne NG+ 5

3. Dark souls 3 NG+ 4

4. Elden Ring NG+ 3

5. Various titles in NG+ (or NG+1 depending on how it's counted)

MGS 1 & 2 is very likely higher but thems the only figures I kept record of. As a kid I'd do a playthrough on those games, roll credits and start instantly right from the start again. One weekend I was sick, I replayed MGS2 6 times just instantly going to a new game as soon as I'd finish and more often than not I'd watch full cutscenes a reliving the story was just as important. To say I was obsessed in a massive understatement, I also spent a massive amount of time, like dozens and dozen of hours re reading magazine article previews and then reviews or any content I could find on the games, even the PS1 Manuel. I wish I had accurate figures cause I know it's higher than those numbers cause I was delving back in with the fat ps3 BC on MGS1 but it's very hazy to remember and I didn't track how much I was playing it being less autistic and OCD as I got older. If I had to guess I'd add on half a dozen playthroughs each, possibly more for MGS2. Oddly, I only played MGS3 as well as MGS4 the once and MGS5 twice. 

No idea because I haven't counted. But Luigi's Mansion and Pikmin, at least a dozen. Same with all the Souls games.

I lost count on VanQuish and Ys 1. Strider 2 and a bunch of 90s games? Esp arcade. Um... hundreds? A lot of games I beat over a dozen times. Some games 50 plus. Others just a few times or once. I don't have exact numbers as I don't keep track.

Longer games: I’ve 100% completed SM64 (5x), SMSunshine (4x), and SMOdyssey (4x).

Shorter games: I’ve 100% completed Pikmin 1+3, Luigi’s Mansion, and OG Super Mario Bros more times than I can count lol.

Shadow of colossus, between the original , hd remaster and remake, probably 16 to 20 times.

Resident evil 5 co op on ps3, probably around the same.

Back in the day, Ninja Gaiden II (one of the few that I owned, as we did not have a lot of money for games), probably a few hundred times. Then Contra, Mario 1, Predator, all on the NES and all in the hundreds. Moving to the SNES, then Street Fighter II for sure, followed by SM World (I would always show people how to use the shortpath to the ending). Coming to 3D, I guess SM64.

Couldnt tell you the amount of times, but Mega Man 2 is definitely the one Ive beaten the most times.

The only one I kinda know is Dark Souls 2 which Ive beaten 9 or 10 times.

Good question. I don't think I've beaten any game (that has some sort of campaign) more than 6 times.

Resident Evil 4 - 2x (GC), 2 x (PS2), 2x (PS3) = 6 times
Chrono Trigger - 3x
Final Fantasy 7 - 3x
Suikoden 2 - 3x
Zelda OoT - 3x
Metal Gear Solid - 3x
Resident Evil 4 Remake - 3x
Metal Gear Solid 2 - 2x
Suikoden 3 - 2x
Final Fantasy X - 2x
Chrono Cross - 2x

All are estimates:

Resident Evil 4 - 30 times (all on GameCube)
Tomb Raider and Tomb Raider II - 25 times each, all secrets (on PS1, PC, and Switch)
Super Mario Bros 3 - 25 times (SNES version, on various consoles)
Super Mario World - 25 times, 96 exits (on various consoles)
Super Mario 64 - 25 times, 120 stars (on various consoles)
Yoshi's Island - 25 times, 100 on all levels (on various consoles)
Super Mario Sunshine - 20 times, 120 Shines (mostly on Gamecube)
Resident Evil 1-3 - 15 times (originals versions, RE1 on PS1, 2-3 on PS1 and Gamecube)
Tomb Raider III - 15 times, all secrets (on PS1, PC and Switch)
Dino Crisis - 10 times (PS1)
Dino Crisis 2 - 10 times (PS1)
Donkey Kong Country - 10 times, 101% (SNES)
Resident Evil (remake) - 10 times (Gamecube)

Then there's something like Tony Hawk's Pro Skater 2 and 3, where I've got 100% on career mode probably 50+ times, although for each individual skater it'll only be 3-4 times at most.

I'm Mr. Replay, so it would take a very long time to make such a list.

But my most replayed game by far is Punch-Out!! for the NES. Hundreds of times across NES, NES Classic Mini, Wii U, 3DS, PC and Switch.