GPS has pretty much had the global location market all to itself ever since it went online in April 1995. Russia's Glonass system works as well as GPS, if not better, but it's only used primarily in that country.
Now, though, GPS will need to prepare for some real competition from a totally new system called Galileo, which is being built by the European Commission and the European Space Agency (ESA).
The ESA launched its first satellite in December 2005, and the first signals were broadcast in January. The system will have from 26 to 30 satellites deployed at 23,000 km, which is just slightly higher than GPS's birds at 20,000 km. Galileo's accuracy is expected to be 1 m or less, compared to GPS's best of 5 m.
The system is expected to be completed and operational in 2008 by some estimates, or as late as 2010 by others. Galileo is a civilian system, while GPS is a military system that's been adopted for civilian uses. It's expected to be more open, and it should find as many, if not more, applications as GPS.