The choice of foundation often depends on where you live.
If you live in a warm climate with a high water table a slab is a common option. It's relatively inexpensive to build, and you get the floor and foundation in one step. But any future repairs or alterations are difficult and expensive.
In mild climates a crawlspace is a great option. The footings go deep enough to get below the frost line and you still have access under the house to easily repair plumbing or electrical issues. We poured a 24" high stem wall on a 10" footing, giving us around 34" to crawl around under the house. Yeah, you still have to crawl, but it's not like you're under there very often. We've only lived in our house 14 years and I've already needed to crawl under to fix a leaky tub drain, run TV cables, run computer network cables, etc. We put a layer of pea gravel in our crawlspace and covered it with a 6 mil poly vapor barrier. If you're in an area where rats or other critters are a problem, you can have a thin "rat slab" poured inside the crawlspace to prevent animals from burrowing up.
In colder climates the footings have to go so deep to get below the frost line that you might as well have a full basement. It's essentially a crawlspace, tall enough to walk around in.
Of course, if you have a high water table or soil that doesn't drain well, keeping water out of a basement can be tricky. It's doable, but it takes a lot of preparation to keep a basement dry.
If you build in a remote area with limited access, or an area prone to flooding, a post and beam foundation may be a smarter choice.
There's no one size fits all solution. You have to evaluate the conditions where you live. In my area (Washington State) crawlspaces are the most common and that's what we chose as well. A full basement would have offered additional living space, but the cost and complexity would have been much more involved.
For small buildings like our shed and pump house, I just poured a simple slab foundation. They don't weigh much and the whole structure can move up and down with frost.