Just moderators, that actually I don't consider as "staff" because they don't have administrative rights, although depending on the contest and the advantage that being a moderator represents over "normal users", I guess sometimes I wouldn't allow moderators to participate. Admins are not allowed to participate.
I let everyone on my forums participate in our contests. I've even entered a few myself. The judging changes with each contest. Sometimes I'll let the moderators vote on a winner, other times I'll create a poll for everyone on the site to vote in, and other times I'll just decide a winner myself. I always make it clear who will be judging before the contest begins though.