Java Edition:Nether Far Lands
From Infdev 20100327 through Beta 1.7.3 existed the well-known Far Lands, one of the most famous Minecraft glitches. This bug caused the very far reaches of your world to become corrupted from bottom to upper bedrock layer. Many types of the Far Lands exist, including the "Corner Far Lands" and the "Farther Lands".
Obtaining
Due to The Far Lands existing in such an early version there aren't many easy ways of reaching them, and you can only do it in survival as creative wasn't added yet.
Travelling
Walking
This is by far the slowest method of reaching the Far Lands as they only start generating 12,550,820 blocks away from 0,0. Sprinting doesn't exist in any of these earlier versions, so it will take a minimum of 5 weeks to reach the edge far lands, and much longer to reach the corner Far Lands.
There is also another way to make the walking process easier. Using the Repeating Spawn Chunks glitch present in Beta 1.7.3, a hole in the bedrock using Java Edition: Unbreakable Block Removal Methods can allow the person travelling to the nether Far Lands to go above and below the nether roof. This makes the journey much more tolerable due to the fact that you only need to traverse a flat plane and not navigate any terrain.
Third Party Tools
Using An NBT Editor
This is by far the fastest method of reaching the Far Lands. All you need is your level.dat file and any NBT editor, simple websites ones such as http://irath96.github.io/webNBT/ will do just fine. Simply edit your coordinates and player dimension, then import the new level.dat file to your world forder and load the world. It might take few tries as player can teleport in blocks and suffocate or die from fall damage.
Single Player Commands Mod
Single Player Commands Mod implements various commands to singleplayer useful for The Far Lands exploration. Recommended are: tele [x] [y] [z], fly, light, noclip.
Other
Commands
Commands weren’t available in Minecraft singleplayer until after the Far Lands were removed, but if you're on a Beta multiplayer server, then you can use the /tp command.
Downgrading
It's possible to get within a few hundred blocks of The Nether Far Lands in newer versions quite easily then simply downgrade to Beta 1.7.3. The chunks will reload and your position will be the same as before downgrading.
Videos
Video by KurrKraft showcasing the Nether Far Lands https://www.youtube.com/watch?v=wtsLlYvb_ak
Video by Xelanater of arriving to the Nether Far Lands (Around hour 3) https://www.youtube.com/watch?v=6yY3QrlBv1o