I always go back.
I just go and start a new game when I feel like it and just run through it all over again just like the first time.

I do it constantly with 2D Platformers.

I always return to completed games. Sometimes I wait until I have forgotten where items and secrets are and then replay again.

Basically never, which is unfortunate. There are plenty of games that I haven't played for years that I'd love to get back to - unfortunately (fortunately?) I have literally hundreds of unplayed/unfinished games on my shelves. I'd much rather go through and finish those before I replay games.

Having said that, there are definitely games that I want to go back and play again some day. Given that I don't buy many games these days, I should eventually get through the ones I already own. When I get to that point, though, I'll be much more likely to replay shorter games, however, than 40-hour-long epics.

I only like to buy games I feel I will be able to play again, platformers are attractive for this reason. The exception being Lego games, I know I'm only going to play them once but I've stopped buying them recently to save the money. So eventually I get around to multiple playthroughs of many of my games especially first party Nintendo.

Almost never.

This. Unless it's River City Ransom, 1943, or Mega Man 2. I could beat those games all day.

Platformers - usually once or twice
Pokémon - anywhere up to about 5 times
Skyrim - Error: Counter Limit Exceeded

I usually replay Mario, Zelda and Kirby games.

I don't replay many games, because I buy EVERYTHING on every console, so I can barely keep up with what's new. But there are a few select titles I tend to replay or plan to replay every couple years.

Usually every 3 years I play through Mega Man 3, being my first video game I ever played and all. I also go back and play F-Zero GX every 6 months or so. And every couple weeks I hold a "retro weekend" where I devote my play to previous generations only. Whether it be VC games, Gamecube, Wii or DS. I also have made a mental note to replay the Metroid Prime trilogy sometime this year. Since those games singlehandedly got me back into gaming, and for the first time as an adult at that.

A perfect game cannot be beaten. Smash you can always get more trophies and stickers, pokemon you can always breed and hunt for shinies, Awakening you can continue to perfect all stats. Only certain games should have a true ending (Zelda, Mario, DK).
That said, I don't replay "beatable" games after beating them like Zelda games because what's the point if you know what's going to happen?
Games like Mario Kart, Animal Crossing, Smash and Pokemon are games that I think nintendo should create more of. Games that can be played for hundreds of hours later or even picked up and played a decade later.

In the last year or so, I find myself going back to Tomb Raider and New Super Mario Bros. U quite a bit, Trine 2 on the PS4 as well.

My most replayed game to completion would have to be Sonic the Hedgehog 2, just because it's such an expertly crafted 2d platformer, and you can fly through it in about 3 and a half hours.

Only RPGs for some reason. The only games I've ever really replayed are Fire Emblem Awakening (but only because I have a huge video game crush on Lucina), and Rune Factory 3. I might end up replaying Rune Factory 4 as well.

Almost never. When I do, it's a game with heavy customization such as Tales of Symphonia or Pokemon, or it's a game with quick levels that can be played in short bursts like Super Mario Galaxy or Plants Vs. Zombies.

Not too often because I barely have enough time to play my new games.
I do play the original Super Mario Bros at least once per year, and I've also played the first and fourth Final Fantasy games (with the various remakes) and the first Golden Sun multiple times.

Depends on the game for me. I generally replay the older games from the NES, SNES, Playstation, PS2 and Gamecube more then the Wii or Xbox 360. Especially NES and SNES. For some reason games from last gen I dont feel the need to replay them once I finish them.

I know the main ones that come to mind that I replay alot are the Mega Man games mainly the ones on the NES.

I feel you with the last gen comment, I think it's because most modern games are just too much of an investment to jump into, dialogue, tutorials, cutscenes, restricted pacing....sure, it makes for superior storytelling in most cases, but the pick up and play factor gets left behind. I've only played Tomb Raider a few times over because The flow of the game is really well done.

Hence why the 8 and 16 bit gens still have that timeless quality, depending on the title.

I almost never replay Nintendo games. Too linear to offer much in the way of replayability ('cept Fire Emblem, I've beaten it twice and have two playthroughs currently going).

It depends on the game. I replay a lot of NES/SNES games like Ninja Gaiden, Mario 3, Actraiser etc., but I also replay some of this gen games, like God of War 3 - I feel like playing it all the time. Same with Ninja Gaiden Sigma/2, Dishonored, Thief, Hitman, Splinter Cell. And strategy games. I rarely replay RPGs.

The replay value depends on the game, and not "restricted pacing", cutscenes or whatever - if I really like the game, I just play it.

any time I feel like it, what's basically all timespan between getting tired of a new game and getting another new game.
so it's almost all the time.