This is not just true in Denmark; the Rhine used to be incredibly polluted back in the 1980s, but now it's pretty clean. The Amsterdam canals are a lot cleaner, though the inner city canals are not used for swimming, but I think that's more an issue of facilities and awareness than of water quality. But in the eastern harbor area, kids love to swim.
The increased water quality is one of the big successes of increased environmental awareness that environmental organizations fought for in the 1980s.