Topic: Video Game Glitches.

Sonic Adventure DX has a lot of glitches, as one would imagine. I remember that if you play as Big, pick up his bed, carry it over to the cliff edge in the Mystic Ruins (jungle) and throw it, it will freeze in midair and slowly float up into the sky (though you have to throw it at just the right spot). It's pretty hilarious! Also, I think if you turn around at the start of Twinkle Circuit, and drive directly into the corner of the track, you can clip out of the track and fall out of the stage. That game is probably full of glitches though, I even remember just running around looking for glitches to exploit but I can't remember any others.

I also know of a glitch in Sonic Adventure 2: Battle. If you're in the Chao Garden (this doesn't work in the Hero or Dark Garden) and you repeatedly use a homing attack (for some reason this glitch will only work if you play as Sonic, using Shadow won't work) at the point between the invisible wall and the rocks, you can clip out of the area completely. You can freely float as far away as you want, and the background is glitched. After a bit, if you float back to the garden, you can walk like normal, but sometimes all of the Chao that were walking on land will be underground. The only thing you can see is their antennae bobbing around as they walk! You can also see the model of the entire garden if you float away from it and then look back, and you can enter the waterfall from the back if you float into it.

tl;dr - Sonic Adventure games have a lot of glitches.

In Harvest Moon Tale of Two Towns, if you plant grains (special seeds which take whole seasons to grow) in winter before spring comes, the plants will go from seeds/whatever stage they were in to full grown ready-to-harvest grains by the second day of spring.

It's a nice glitch.

Oh! from the same game...
If you go on a date with a marriage candidatw on a half-sunny-half-raining day and select a dating spot where other people would normally be at the same time, you'll see floating umbrellas where they should be standing. The game hides other people when you're on a date, but not their umbrellas!

I'm surprised no one mentioned the bottle glitch in Zelda: OoT(64)...
You can turn an item into a bottle. Use the bottle to put something inside, then right when Link is about to hold up the bottle to say what's inside, press pause, and switch the bottle item on whichever c-button it's on with another item.
I don't think this works on the 3DS remake, or Majora's Mask. I used to use this glitch to have tons of fairys for whatever reason. I would replace Deku seeds, the chu-chu bombs, the event item(claim check) after getting biggoron sword, and the mask with a bottle.
You can over ride the glitch by picking up the item again. So you can buy chu chu bombs to get them back, get a mask from the Happy Mask guy, or find Deku nuts laying around. The only ones you can't fix are the godess powers, and the last biggoron sword event item, I think.

Oh ya, and every Tony Hawk game has game zone glitches. In Tony Hawk Pro Skater 4, go to the alcatraz prison level. There are 2 bowls near the top of the island, next to a water tower. Jump off that area into the 'dead' zone by the water tower. The game will respawn you doing the falling motion in the bowl. You can still hear the skating sounds, but you can't move, and the falling animation keeps repeating.

In Tony Hawks American Wasteland. Go to L.A.(I think. The one with a highway corridor thing in the middle of the stage). Go to the area where there is a circular pedestal, and jump in between the buildings on the roof. You will see an alley way. Jump into the alleyway(this is near one of the dead zones on that corridor highway), and continue onward by dodging the ground without shadows(seriously). You will eventually go through some walls, and see what looks like an endless pier made out of grass.
You can still do more with this glitch. Go into the corner of the pier looking area, and jump. If you do it right, you'll keep floating around, and will either take forever to land, or will never land. If you fall off you board in midair, it will do the falling animation, but it isn't continuous and your character will freeze.

The only other glitch I can think of is in the Super Mario World(Wii U VC version). If you are doing a spin break through a big area of blocks, have a cape(use it to float), and are using the run button. You can teleport through blocks.

I know what you mean there. The game has quite a few major glitches in it.

Like that key glitch in ScareScraper which randomly causes a key to fail to spawn in a room where it should be present. That really sucks.

Or the instance where I managed to get stuck in the floor somehow by falling on top of an object in the Treacherous Mansion Dark Ages Exhibit:

I also managed to get locked out the Nautical Exhibit somehow. You know, on that tiny pirate ship platform stuck on the outside of the building thanks to have some object knocked off the switch that holds the ship wheel down.

There's also this amusing bug someone encountered in the game:

But yes, plenty of glitches and bugs in Luigi's Mansion Dark Moon.