How do I get the end of the world?

In older versions of Minecraft there was an edge of the map called the Far Lands. However, since Beta 1.8, the Far Lands act a bit differently:

In [Beta] 1.8, instead of the Far Lands starting to generate at 12,550,820 meters from the center of the map, the playable area abruptly ends at 30,000,000 meters, and fake chunks (they are not solid, they can be fallen through) start generating. A sure sign that one has reached the edge of the map is that lighting no longer works past the 30,000,000th mark. Versions between Alpha 1.2.0 (Halloween Update) and Beta 1.7.3 rendered fake chunks outside of a limit of 32,000,000 meters; attempting to walk onto them would cause the player to die in the Void. From the beginning of Infdev all the way to the Halloween Update, the world abruptly ended at 32,000,000 meters, and leaving the boundary caused you to be trapped rather than die.

To get to the 'Far Lands' you can follow the instructions in the Minecraft Wikia. However, as it says in the first sentence there is no easy way to get to the edge without using commands or external programs (Though there is a long running series that attempts to walk to the Far Lands, he is currently on episode 255). It is also prone to make your Minecraft crash so try it at your own risk.

Getting to the Far Lands without the use of an external program was a very difficult (or at least time consuming) task, as walking to there from the center of the map would have taken approximately 820 hours (or 34 days). Instead, a level.dat editor could be used to teleport the player there.

The boundary between the normal map and the Far Lands (defined by when the map started generating the distorted terrain) occurred at X/Z of ±12,550,821.

The hard limit where chunks are overwritten is at X/Z of ±34,359,738,368, which is about 23% of the distance from the Earth to the Sun. At X/Z of ±2,147,483,648 (crashes at 2,147,483,439), item positions, mob pathfinding and other things using 32-bit integers will overflow and act strangely, usually resulting in Minecraft crashing.

At X/Z of ±1.798*10³⁰⁸, the position of the player, represented by a double-precision floating point number, would overflow to 'infinity', causing a complete breakdown of arithmetic. Even at far smaller coordinates, the limited precision would cause errors in calculations. For example, at 10¹⁶, xPosition + 1 is equal to xPosition.

Using Single Player Commands, it is very easy to get to the Far Lands using teleportation. After pressing the chat key (default "T") to open up the console-like input window, using the "teleport" command (or its abbreviation, "tp") followed by X, Y, and Z coordinates will allow the player to go wherever they want. In Release 1.3, you can turn on cheats to teleport. For example:

To get to where the Edge Far Lands' wall was, try "/tp 12550820 129 0". Make sure either flying is turned on or damage is turned off, as otherwise you'll fall to your death. To get to where the Corner Far Lands were (the walls' intersection), try "/tp 12550820 129 12550820". Again, make sure you're protected from fall damage.

Unfortunately, there was severe lag, and slower computers used to crash upon this teleportation. Opening a GUI helped the Far Lands render much, much faster. You can do this by pausing (pressing Escape) or opening the Single Player Commands prompt again. When you venture out farther above and into the far lands, the probability increases that a "bad chunk" will appear. A bad chunk is a chunk filled with terribly corrupt data, and is the cause of sudden lag spikes that can easily make Minecraft crash.

Here is a question related to the Far Lands

Unfortunately, most of these answers are outdated, so here's one from 1.8.

You can reach the end of the world, but it requires teleporting. At the end of the world, you are met with the World Border.

This can only be crossed on one side, and that is to get in, not out. The only way to get past the WorldBorder is to use the /tp (playername) 29999999 100 29999999 command. (Note, do NOT try to walk. If you need to prove this yourself, teleport. Here's why:)

If you end up teleporting outside, you can fly back. There isn't much to do here. If you want to fall out of the world, You can't. Sorry, but another, invisible, world border greets you. Unfortunately, if you were to teleport outside, that would be the limit to how far you can teleport. You would just get an error message and a dilemma.

Other than curiosity, there is no real reason to be here. Because of the dangers of players breaking the world border, you can place blocks, but not break them.