Redmine Events lets you create signup forms for events. The signup forms can be created from a combination of any number of custom fields defined in the project settings, the form is pre-populated for logged-in users.
This is currently at best an alpha release! There are currently no permissions enforced on any part of this plugin, i.e. everyone can access every part of it, there is currently no separate "admin" (full details) and "public" (lesser details) view of the list of signups, meaning everyone can see everything entered in the forms, and other stuff is probably missing too. This release is only meant as a developer/tinkerer preview of sorts and is by not production-ready by any means.