I think there is a difference between "mysticism" and "being a mystic". I think the OP was more directed at mysticism in Christianity generally, so I'll address that (besides, it's what I'm personally more interested in).
First, a definition... when I think of Christian mysticism, what come to my mind are things like the real presence in the Eucharist (a belief held by Orthodox, Catholics, Lutherans, and Episcopalians), visions (prophetic and otherwise), and the Orthodox doctrine of theosis, which involves sharing in God's energies (but not in His essence).
In my experience, there is precious little mysticism in Protestant christianity. Indeed, it seems to me that protestantism as a whole rejects mysticism outright. (The Charismatic movement is probably an exception to this, but I don't know much about it). Protestants (other than Lutherans and Episcopalians) do not believe in the real presence and, generally speaking, avoid a sacramental (i.e., a mystical) understanding of practices like baptism, marriage, etc.
In fact, it is this very lack of mysticism that is prompting me to leave Protestant Christianity for Orthodox Christianity. I think there is a place for the mystical in everyday Christian life, without being some hermit off in the woods.