What is the fastest way to travel in Minecraft using non-standard means?

Solution 1:

You can boost a thrown Ender Pearl using a TNT cannon. Assuming you've got the trajectory exactly right and have a wall at the destination to stop the pearl, this is basically instantaneous other than the fuse time (4 seconds). Also, in one step you can only travel as far as the chunk load distance, which as far as I've read is 160m (10 chunks), or else the pearl will not land until you move closer. So, speed: 40 m/s average, less time to gather resources and place the TNT, and the flight time of the pearl (which will depend on the amount of TNT used and exact trajectory).

If you built a series of redstone-driven TNT magazines wired to operate in sequence and launched pearls perfectly to match them, then you could avoid waiting 4 seconds and move even faster.

Solution 2:

In vanilla, single-player minecraft, the fastest way to travel any distance is to use command blocks to set up teleports. These will send you any distance in any direction instantly.

While command blocks are vanilla, they are not possible to get in a non-cheat-enabled game. You need to be in creative gamemode and have access to the /give command to obtain them without mods. If your world has cheats enabled or you are willing to use an external program to assist in getting the command blocks set up, then they will work just fine in vanilla from then on.

To get the command block and give yourself the ability to set it up, enter the following in chat:

/gamemode creative @p
/give @p 137

Place the command blocks where you want them and use them to teleport near each other. For example, if you have one (which I'll call A) at (x,y,z)=(0,5,0) and the other at (x,y,z)=(200,5,0) (which I'll call B,) then right click on command block A and type

 tp @p 200 5 5

into the command field. Similarly, in command block B's field, use

 tp @p 0 5 5

Note that in each case, I've put the teleport "landing zone" +5 Z-blocks from the other command block. Now place a stone pressure plate on top of each and step on it. You'll be instantly sent to the vicinity of the other.

To return to survival mode, use:

 /gamemode survival @p

I've created a small (~300k) demo map demonstrating this that you can try out in vanilla Minecraft 1.4.7.

Solution 3:

This YouTuber is going 47.4 blocks per second. I've tried it myself too, works okay. I'm getting 43.1 b/s.

In this video he placed Minecarts every 3 blocks to be able to spam right-click, teleporting to the next minecart in front of him every right-click. That way, by spamming rightclick, he got very fast. 47.4 m/s he got, I am getting to 43.1 b/s.