To answer the first part of your question, have historically multiple spacecraft launched on the same date from geographically distinct locations, yes. In fact, it just happened last Wednesday, September 18, 2013 when two rockets were launched on the same date, and both from different facilities in the United States:
Since space launches are becoming rather frequent events in recent history, I'm pretty sure there were many other instances of two or more launches on the same day, so I'm just going to additionally mention the Apollo-Soyuz Test Project for its historical significance, during which both launch vehicles (Apollo CSM-111 and Soyuz 7K-TM) also launched on the same day, July 15, 1975, from Kennedy Space Center and Baikonur Cosmodrome, respectively.
As for the other part of your question, if there is a global body to coordinate such multiple space launch events, I would have to say no. Not a global body and not really coordinating it, but there would of course be local or nationwide bodies regulating airspace activities, and when rocket launches cover international airspace, coordination between all involved jurisdictions would have to take place and give clearance for the launch to proceed at any pre-designated time frame (launch window).
Additionally, there is The United Nations Register of Objects Launched into Outer Space, set in motion under the Resolution 3235 of the UN General Assembly, and possibly other international / global registers that all launch systems under their jurisdiction would have to report to, but I'm not aware of any that would also coordinate various launch site activities on a global scale.
For what it's worth, we covered both of these two events mentioned in The Pod Bay, our main chat room, where we posted links to live broadcasts for the events and had a chat observing them unfold. Our main chat room's schedule is also the place to look at for future chat room events, on top of featured events also being displayed in the Community Bulletin box on the right side to every Space Exploration SE main site page with a convenient countdown displayed next to each scheduled event. The chat room's schedule also includes your local times for any currently scheduled events and an option to register for events with an email notification sent to your address a few hours beforehand as a reminder.