How long does it typically take to get a US Passport?

I think it depends on the time of year and possibly where you are. My father told me it would take 2 months but I got mine in about 4 weeks.

It'll take long enough to make you worry. My family was going was going to have to get them to go to Canada a couple of years ago, and we heard about the possibility of having to wait a couple of months. I think my dad heard somewhere that if you signed up under certain conditions, they could be done in about 2 weeks. Then, we found out that we didn't need them to go to Canada at that point, so we never actually got them...

I'd suggest applying a couple of months before your trip is scheduled. You can spring for the fast processing, but it's not really worth it, in my opinion. Enjoy your trip! Sweden is beautiful in the winter, but you should definitely go see it in the summer, too.