Minecraft wiki entry for Transportation, associated text: Players are also able to use pistons for transport.
It is possible to construct complex flying machines using pistons, blocks of redstone, slime blocks, and honey blocks.
Dying is an instant mode of transportation to the player's bed or spawn point, but at the cost of all items and XP (if the keepInventory gamerule is disabled) and the world (on Hardcore).
If the player has already defeated the ender dragon, and is near a stronghold/end portal, they can enter and exit the End to instantly be transported to their bed or spawn point without dying.
Explosion knockback can send an adjacent player flying for a short distance, depending on the strength of the explosion. This is not recommended in Survival mode.
It is possible to mount minecarts and boats as long as they are within 4-5 blocks (inclusive) from the player. Placing these in a straight line allows for extremely fast transport. This also works with saddled pigs, provided they stay in position (placed on posts).