In case you're wondering, Galileo will use a similar transmission standard to GPS, so you will be able to use both systems on the same hardware.
Of course 2013 is five years away, which is an eternity in the mobile electronics world. It is possible that by then GPS phones will be far more sensitive than they are now, but even so it will presumably still be an advantage to have two constellations to refer to instead of just one.
More accurate indoor satellite navigation could have implications for pedestrian navigation, for example shopping centres might include their indoor layout on navigational maps.
Whether there's a real technical need for a second satnav system is debatable, but the geopolitical need seems to be in the driving seat. Many in the European Union government (the EU are paying for Galileo) want to make themselves seem important, and present themselves as an alternative to the US on the global stage. At the moment America is the only country to operate a satellite navigation constellation, and this is why people use "GPS" and "satellite navigation" interchangably, even though GPS is just the American system.
There's also a military significance in Galileo: At present the US government may selectively distort the GPS signal in regions where they don't want the enemy to be able to use satellite navigation, but if Galileo goes online the US will have to convince the EU to co-operate in any such distortion.
And that's not all. There's a third sat nav system on the way too, the rather unfortunately-named GLONASS, which was built by the Soviet Union (later Russia) but left to rot when the money ran out. Now that Russia is on the way up again economically, the system is being restored with a target date of 2010 for global coverage. It will be compatible with Galileo and GPS, and Russia has said the system will be open to the public, so future mobile devices will have three constellations to receive signals from instead of just the current one.