They're pretty common. You definitely have to watch out for them when driving in the countryside. I googled it and in the summertime there are 300 000-400 000 moose in Sweden.
Wikipedia gave me this interesting tidbit that I feel I have to share: in Denmark, they've only had one known moose so far. It swam over from Sweden July 14th 1999. The Danish society for protecting animals promptly set up a moose warning sign much like the ones we have here, in Humlebæk where the moose lived. Unfortunately the poor creature was killed by a train the following year, so now they're moose-less again.