Simply put: Vulcans did not have interest in space. For a society where greatest challenge, honour and reward are self-improvement and seeking perfection, service on a spacefaring vessel would be hindrance rather than help in attaining those goals. Any shipboard duty leaves rather small amount of free time; just ask anybody with experience in navy.
And as always, there are exceptions. Obviously.
And no, Starfleet did not encourage homogeneous crews (DS9 case of all-Vulcan ship was special dispensation IIRC), as is implied in other answer. I don't know if ENT finally made canon, but even with that discarded, it's clear that Federation came to be as a solution to one-race-crew-ships problems in the first place.
Somewhat different was diplomatic/political service — those offered better opportunities to perfect oneself (patience and smell, especially), and were much less time-intensive. So they could be viewed more favourably.
EDIT: Eating a frog here. It seems that canon indeed allows, even insists on segregated crews (from Gene Roddenberry himself: https://i.stack.imgur.com/yHln0.jpg).
Shows how much problems creates sticking to the rules invented so long ago that no one remembers them.