From Sweden there are two ferries to Denmark from Helsingborg to Helsingør. You can actually see Denmark from Sweden and Sweden from Denmark on this short stretch. (in clear weather of course). There are 3 services to choose from:
HH Ferries at HH Ferries
Scanline at Scanlines
There are two other services from Sweden run by Stena Lines.
Göteborg to Frederikshavn and Varberg to Grenaa StenaLine Journey time is 3.5 hours and 5.5 hours respectively.