According to one of the professors at the University of Navarra (where I was teaching), Spain does not have a long-term disposal site for high level nuclear waste. Neither does the United States. The Yucca Mountain site was supposed to act as a long-term repository, but various studies about the seismic safety of Yucca Mountain and politics led the Obama Administration to withdraw the permit application for Yucca Mountain. Spain's basically in the same place: power plants keep producing nuclear waste but development of a long term disposal site is way off.
There are many potential problems associated with nuclear waste storage, and the Japan disaster highlights one of the biggest risks. As various news outlets (including the New York Times) report, experts are particularly concerned about the spent fuel rods overheating because the rods, unlike the nuclear reactors themselves, are not encased within containments designed to prevent releases of radioactive materials. Releases of radiation from the spent fuels would therefore be almost impossible to control. Even if Japan somehow manages to gain control over the nuclear reactors (something that seems increasingly unlikely to happen), that may not prevent catastrophe with the spent fuel itself.
Nuclear energy advocates in Spain and the United States have argued that such a catastrophe would not occur elsewhere. They argue that the 9.0 earthquake and tsunami are extreme, outlying events that we should disregard in assessing safety in other areas.
I think I prefer The Onion's perspective: Nuclear Energy Advocates Insist U.S. Reactors Completely Safe Unless Something Bad Happens
I was actually interviewed by a news channel in Navarra about this. For anyone interested (it's in Spanish, thanks to my translator,
navarra/noticia-experta-dice- debate-energia-nuclear-mas- politico-seguridad- 20110316182810.html