I have a relative who adopts greyhounds, and has probably owned close to a dozen total dogs over the years. He currently has three. You typically will get them when they are a few years old, sometimes toward the ends of their lives, so on the one hand, they tend to be calmed down a bit, and less puppyish (although they can still run). On the other hand, they are old enough to be set in their ways, so training them specifically as a trail dog that will obediently hike with you off leash is going to be near-impossible. I cannot speak to their endurance, as my relative doesn't hike too much.
If you want a trail dog specifically, I'd recommend a dog of medium to medium-large build, with medium length, slender legs but strong shoulders, short to medium length fur (ticks are a bitch to find in long, shaggy or knotty fur), and a temperament known for obedience. Hunting dogs and bird dogs tend to make good trail dogs as a rule, but even then, not all breeds are the same. Greyhounds are a little too large for slow trail walking, while corgis are a little too small for long distance endurance (
>>454146 looks like an absolutely tortured animal). As for temperament, what you don't want is a dog that is going to be overly nervous or overly curious. Golden retrievers tend to be incredibly calm natured and obedient, although their hair is borderline too long for keeping them relatively groomed on the trail.
