Can users create events?

Each event is a WordPress post, so any user that has permission to access the dashboard and create a post can create an event. More information about user roles here: http://codex.wordpress.org/Roles_and_Capabilities

NOTE: There are some plugins out there that allow users to create posts from the front-end of the site without needing to be a registered user, but I haven’t tested any of these plugins, so I don’t know if they would work well or not.