I saw a squirrel (ekorre in Swedish) the other day, leaping around the rocks. And Grant saw a red deer on our land; it scampered away before I could get a look. (Sooz, when told, said, "Oh great. More ticks.")
Lastly, Dave had told me of the giant island rabbits, or more accurately hares, which are bigger than dogs. Sure enough, I saw one and it was as huge as Dave described.
The one animal we haven't seen is the järv, which Janne told us about last winter. Not sure if I'd like to see one; I'd rather see a moose.