What is the fastest way to travel long distances in Minecraft?

Well, the fastest form of transportation is by minecart, and within The Nether you travel at a 8:1 ratio as in the overworld, so my answer would be traveling via minecart in The Nether.

(Even walking in The Nether is faster than any overworld transportation - minecarts top out at 8m/s, and you certainly walk faster than 1m/s.)

As Kevin says, use The Nether. The only problem is that it's often dangerous.

As for "the fastest way to travel long distances", the objective answer is: Teleboaters. Minecarts come a distant second. As for construction, tracks cost 1 iron per 2.7 squares of travel, not counting boosters. Teleboats cost 1 log per ~3 squares of travel. But boats are hard to carry and look terrible.

(Fun fact: the truly fastest mode of transport involves a giant stack of simultaneously-triggered TNT.)

With the introduction to horses, riding a horse through the Nether is currently the fastest method of travel. It is also more versatile, can traverse raw terrain easier, and is not limited to tracks.

If you want to explore a completely new area, bring along 10 obsidian + flint & steel, travel by horse for a few minutes in the Nether, plop down an exit portal and you have a fresh, brand new area.