There are many types of transportation you can find in your blocky world-Donkeys,Steam Trains,Jetpacks,etc.
Donkey:Spawns near carrots whether planted by player or naturally spawned. To ride a donkey you need a Carrot on a Stick to ride it, and only if they are fully grown because they may spawn as babies.
Steam Train:In Construction
Jetpack:You can make it in the the Level 4 Craftbench.
To make it:Use 2 Carbon Fiber wings,A Jetpack Chassis,2 Jet Engines and 10 fuel.
Boat:You can make it in the Level 2 Craftbench
To make it:Use 2 Linen and 2 Wood