What plugins (especially unofficial) are you running?
Did you install Discourse via the Official Instructions? If not, how did you install it?
Any errors in your site logs (/logs)?
Is your site public? If so, can you share a link?
Best guess is there’s a plugin incompatibility, or other configuration issue. User profiles work just fine here on Meta, as well as try.discourse.org, both of which are running the very latest code.