Super Events is an event management plugin with RSVP.
Super events does two major things.
Creates an event type, as a custom post type. There is also a type taxonomy associated with the event post type. This will help you categorize events by type - E.g. weekly meeting, Special events, Guest speakers, etc.
Creates a sidebar widget for RSVP. You can drag this widget to any of your sidebars. This widget will appear ONLY on event type pages. The widget allows the user to enter a response (yes, no, may be) if logged in, else points a link to login/register. If the user has already set a RSVP, the user may update it here too.