Meetup is a great example of a event system.
A calendar would make it really nice.
I'm not saying this will happen, but my grand vision is how cool would it be if we could create a social media site that is addicting not by how much time they spend using the site, but rather a great resource that allows like minded people to meet up and easily coordinate when and where. This in turn will increase satisfaction, make the site more popular, and increase "real world" productivity that will bring people together face to face.
This summer I have tons of climbs lined up. It's hard for my friends to know exactly when they can see me or join me for an adventure. Using a combination of events and the calendar app I could theoretically fill out the dates (and date ranges) that I'm busy. Again, the idea is to combine the values from the app and events into one centralized location. With a click of a button the user could click a date (option appears on hover) that they would like to see me. I could either accept or decline it. If we got really fancy we could have a way for me to reply back to that user (using ES's native pm system). Think of it like a very speedy way of telling your friend "hey can I see you this Friday?". This would make coordinating times so much easier for both the requester and the receiver!
Then if we had re-occurring calendar items like a work schedule, this would cut a lot more work off the user. At that point the only thing they would need to do is make sure they reserved enough time for themselves.
Back on the topic of events. One of the down falls of facebook is that events have no sorting mechanism, as in I see "random" events from friends that are kinda distant. In turn this reduces the usefulness of checking for up coming events. So if the user could give criteria for what events to display for upcoming (category, weekends only, friend events only) that would help a lot. If the admin/poster allows it, users should be able to search for events outside their friends. This allows people to reach out to meet new people.