I'm Bringin' Glitchy Back

Super Mario Maker: Psycrow's Glitches! The Tutorial Video(s)
Important note: You don't have to go back to 1.0 anymore since I found a new Black Hole technique recently (and someone found an even quicker way after that). All glitches still work in the latest version of Mario Maker (currently 1.47 at the time of this edit). Videos on this page are generally showcased/hosted by others, with any below generally being various level showcases; if anyone has questions or comments, email me at themindhero(at)gmail(dot)com. New: Here's how to get modded items into Mario Maker, and some tips on memory modding!
Playlist showing glitches taught in the first video above
Playlist shows prior glitch level showcases, which make use of all glitches taught in the tutorial video above: 1.0 glitches revived, the Game Genie technique (thinks-it's-on-a-track), the Black Hole Technique, Thinks-it's-in-a-pipe/cloud/clown car, Teleportation, Giant/mini cars, Walk-on-lava, Invisible tracks, Item-on-track-with-key and Cloudless Lakitu. A few levels seen here use techniques which were not found in time for the tutorial video, but which (unlike most of the ones in that video) mostly required staying in 1.0 even if you have a glitched Thwomp, and are hard to explain by text. But one you can do easily in the current version is to take a thinks-it's-on-a-track item, like a skull raft or blue platform; place another item like a Door one tile above it; Select Area to grab both at once; and drag the door to the bottom of the screen (where an empty pit is), so that the thinks-it's-on-a-track item is 1 tile below the screen but the door is on the bottom tile, and let go. The door will pop back to where it was, but the glitched item will stay 1 tile below the screen. If you let a cannon sit above it, in the case of the skull raft for example, the cannon would appear to be sitting on the bottom border; in the case of the blue platform, for some reason that goes 2 tiles below the screen instead of 1 (normally impossible to save into a level) even when just getting it 1 tile below the screen, so if cannons/sideways springs/etc drop on that and Mario walks on that area, you've got Mario walking on the bottom border of the screen himself. Also in 1.0, try dragging a Clown Car that's on a tracks to an area where red squares appear (indicating you can't put it there), then let go -- part of the track will move away. The last video in the playlist above shows some use for this (in the second half).
Levels made with memory modding (and later some graphic modding)

Playlist shows prior glitch level showcases, which make use of all glitches taught in the tutorial video above: 1.0 glitches revived, the Game Genie technique (thinks-it's-on-a-track), the Black Hole Technique, Thinks-it's-in-a-pipe/cloud/clown car, Teleportation, Giant/mini cars, Walk-on-lava, Invisible tracks, Item-on-track-with-key and Cloudless Lakitu.

A few levels seen here use techniques which were not found in time for the tutorial video, but which (unlike most of the ones in that video) mostly required staying in 1.0 even if you have a glitched Thwomp, and are hard to explain by text. But one you can do easily in the current version is to take a thinks-it's-on-a-track item, like a skull raft or blue platform; place another item like a Door one tile above it; Select Area to grab both at once; and drag the door to the bottom of the screen (where an empty pit is), so that the thinks-it's-on-a-track item is 1 tile below the screen but the door is on the bottom tile, and let go. The door will pop back to where it was, but the glitched item will stay 1 tile below the screen. If you let a cannon sit above it, in the case of the skull raft for example, the cannon would appear to be sitting on the bottom border; in the case of the blue platform, for some reason that goes *2* tiles below the screen instead of 1 (normally impossible to save into a level) even when just getting it 1 tile below the screen, so if cannons/sideways springs/etc drop on that and Mario walks on that area, you've got Mario walking on the bottom border of the screen himself.
Also in 1.0, try dragging a Clown Car that's on a tracks to an area where red squares appear (indicating you can't put it there), then let go -- part of the track will move away. The last video in the playlist above shows some use for this (in the second half).