The ideal would be a unified global network controlled by a non-partisan body (the UN perhaps, or a multinational infrastructure cartel like the ones that lay submarine cables). Maybe in 50 years we'll reach that level.
Of course, this is all assuming that Galileo, the ESA's GPS alternative, gets off the ground. After the Iraq debacle, Britain is unlikely to support it for one (the Blair administration has been outspoken in condemning multipolarism, and given that Washington is unhappy with potential challenges to its supremacy, London probably won't hurry to pay its share of the Galileo bills, and may even attempt to scrap it); meanwhile, the system is mired in the usual Eurobureaucracy, with international squabbling over funding halting work. And if they wish to go ahead, they'd better hurry; the frequencies allocated to Galileo by the ITU will be forfeited if a satellite isn't launched by 2005.
Spy satellites are easy: one by itself will be useful. Navigation satellites require a cluster of 24 or so (like GPS) to be reliable and have good coverage. I doubt whether Japan, Israel, India or whoever would have their own GPS-like satnav clusters.
China has also been launching "navigation and positioning" satellites: http://english.peopledaily.com.cn/200305/25/eng20030525_117171.shtml
I believe even US allies like Japan and Israel are putting up their own spy satellites in order to have an independent source of intelligence.