This is a bit retro, but I love the "Screen Warp" in Legend of Zelda: Link's Awakening.

It can make the game look really weird if you use it in the right places, because you can take other characters/monsters to places they shouldn't, and more often than not other characters and monsters will have the wrong graphic or something, and if your inside certain places you can go from one interior location to the other even if they're miles away from each other (I guess all the interiors are on the same file for the developers?), and you can do other weird things too, like if you use it in a particular place it will put you in a "glitch world" which are basically several interior locations, but messed up, and you can "swim" through the walls to get to each one - it is weird. I might list examples of the "glitched worlds" one day.

If you don't know how to Screen Warp, you press Select to bring up the map just as you cross over to the next screen - if you do it right, you will be on the opposite side to where you should be, and if you use it in the right place, things might happen. This will not work on the DX version, and there are some copies of the original that don't have this glitch as well, I think (the older it is the most likely it is to have it, I think).