http://en.wikipedia.org/wiki/NemID
Most public institutions as well as many private (including the banks) have switched to this system.
Our government already know just about everything about us (e.g. few people need to fill out tax forms), so this has not been very controversial. The largest controversy has been with the security.
Actually I don't get why the gov makes people do one in the US and Canada. Most people have their income reported to the gov by their employer. That information should be downloadable by people and then what is missing could be filled in, mistakes fixed, deductions not already calculated added...
Until recently, a lot of SK banks also used ActiveX plugins for "security" instead of SSL, making it basically impossible to use anything other than Internet Explorer. I get the impression this is changing.
I wouldn't trust the government to handle identification across multiple sites any more than I trust Facebook or Google.
The UK has a similar system, although surprisingly few people know about it: http://www.gateway.gov.uk/
If it's only intended to be used in this kind of way, no problem. If not...
http://en.wikipedia.org/wiki/National_identification_number#...
I've got to say, having a personnummer makes dealing with the Government and businesses a bit smoother and more efficient.