Absolutely need this feature. We have lots of free and pay-at-the-door events and we would use this feature all the time.
It makes sense to put this into the member profile and allow them to cancel any free event they have registered for.
In addition, I'd like to see an "evite" type of option to have members RSVP for events with Yes, Maybe or No. I also like the ability to send emails to members of a group based on their RSVP status - e.g. send to all "Yeses", all "Nos", All "Maybes", All those who haven't RSVP'd.