READ BEFORE READING: I know this may be part of some mod already, but mods tend to conflict with each other so often I'd rather have it in vanilla.
I sometimes get rather pissed after strolling the wilderness for two hours, noticing my rather small inventory is full of whatever I've been gathering (usually clay) and having to waste another hour on walking back home to get rid of it. Thus, carriages began to seem like a rather attractive idea...
How they would work:
Carriages could be drawn by one to four pigs (at least up until horses are added to the game). The pigs are powered by feeding them wheat (in a similar fashion to a powered minecart) and while out of wheat they will refuse to continue. Steering would be similar to steering a boat, though due to its size the carriage wouldn't be quite as maneuvrable. Carriages would end up 2 blocks wide, 3 blocks long and 2 blocks high, and could climb uneven ground 1 block up or down at a time similarly to minecarts.
How they would be crafted:
First of all, a carriage would need 4 wheels. Wheels would be crafted as follows:
This would produce 2 wheels. The carriage itself would consist of a front end and a rear end, crafted as follows.
Combining a front end with 2 wheels on each side of it would yield a front half carriage, and a rear end with 2 wheels on each side a rear half carriage. The rear half carriage could be equipped with 1 or 2 chests, while the front half carriage could be equipped with a crafting table and a furnace. Adding any of these to the carriage would slow it down due to weight, but contents of the chests wouldn't. When the desired equipment has been added, the rear half and the front half could be combined to form a carriage.
When a carriage has been placed on the ground, it can't be broken to take the whole carriage into your inventory again. Instead it will, similarly to a boat, yield a number of wooden planks and sticks smaller than the amount initially used to craft it, as well as the possible contents of chests and the chests/furnace/workbench that was/were on the carriage.
To attach pigs to a carriage, one would have to saddle them, ride them near the carriage and right click on it. Each additional pig would speed up the carriage but also make it less maneuvrable.
Better Than The Cars Idea... But No, No Roads Please! For The Sake Of Minecarts. If Roads Are Added, This Means Transport War...
It wouldn't require a road. I meant this mainly for exploring the world and/or settling elsewhere if you get bored of your old house. In both cases you would, probably, only ever make the same trip once or twice, so roads would be pointless. The carriages would be more like, well, off-road.
Also as you will have noticed, the carriages would require saddled pigs, and as long as saddles can't be crafted these would remain so rare the majority of the people in SMP wouldn't be able to get these, so a road network would hardly emerge.