When I'm riding a motorcycle to a far away destination or running a trail on some mountain, I'm doing it to ride a motorcycle or to go for a run. I don't mind being alone, most likely even enjoy it, but that's not what I'm out there for. The exception could be sitting on a meditation cushion, but to me aloneness (EDIT: in the case of meditation) is more of a requirement than a goal.
With all that said, I do have a teensy nit to pick with the title: alone != lonely. Sometimes the two intersect, but not as a rule.