No, it is possible, but you cant do it entirely. Its called the pan american highway-
http://en.wikipedia.org/wiki/Pan-America…
Theres a section from Central America to South America called the darien gap-
http://en.wikipedia.org/wiki/Dari%C3%A9n… that is all swamp and rain forest that they simply dont have the money to build a bridge for- so you would have to pay a ferry to take the vehicle and yourself across it- I hear its not hard.
You just need your passport, wont be a problem going between the borders. I hope you do it, and post a blog about it- it sounds fun and Id love to do it myself, but the cost would far outweigh me ever being able to do it.
The goal is that one day, they will have a road from Moscow, Russia over the Bering Sea on a bridge into Alaska, then a highway all the way to Mexico, and road the rest of the way therebye connecting both continents.
How would you carry all your stuff on a motorcycle though? That would be the issue- you probably would need to do this in a car.