you certainly can - but it's rather expensive and bit of a pain. Crating and shipping will run roughly $600-700 one-way to ship across the US. Much more $$$ to/from outside the continental US because of customs, etc.
Also, it's much better to do the other way around (ride to destination, ship back), for several reasons. For one, unfortunate things often happen during shipping. Things get lost, delayed, or damaged. Better to have that happen at the end of your trip than at the start. Your trip could end before it even begins. Or, you could be wasting valuable vacation time waiting because of a delay.
The other main reason is psychological. Slabbing hundreds or even thousands of miles on the highway sucks. But, it is much more tolerable on the way to a destination than it is on the way back. On the way out, you're body is fresh and you're excited about what's to come. On the way home, you're exhausted, you're thinking about having to go back to work or other things that will need you're attention. You've just experienced the splendor of Alaska or Moab, and now you have to get back to the "civilized" world. That long trek back home is always a real downer for me.