The vertical separation in en route airspace is 1,000 feet. That is not so much a GPS factor as it is advances in altimetry. The 1,000-foot separation has been in use now for probably a decade around the world, and I'm not aware of any incidents. When it comes to the safety standards that have to be met by the regulators that certify this, including Canada, the U.S., ICAO, and all the other countries, some pretty rigorous mathematics are applied to that. I'm not aware of any incidents involving it.
On May 31st, 2012. See this statement in context.