When I first arrived in Copenhagen I struggled to figure out what to call the water channel that divides the island of Amager from central Copenhagen. It is counter intuitive, but the name the Danes have for it is the harbor, and a harbor it is.
Environmental projects over the last century have invested heavily in cleaning up the harbor. They've paid off and it is now so clean that you can (and locals regularly do) swim in it. Though for safety reasons, swimming is limited to specific areas.
One of my favorite ways to see the harbor is to take one of the water buses (included in a normal metro ticket) the length of the harbor. It lets you see a lot of the big sights in the city while relaxing all for the price of a metro ticket.