Yes its an Old Town, and yes there are so many like it in Europe. And yet, Copenhagen has a beautiful Old Town that, unlike so many others, put me in a really good mood each time I walked through.
The main street, Stroget, is crowded with tourists and international chain stores like Disney and Abercrombie and Fitch. The streets behind that, though, are full of great restaurant/bookshops/cafes/buskers.
I also happened to be in Copenhagen during Jazz Week, which involved a lot of private gigs but also as a lot of open-air performances put on for the public. The sound of good music coming out of an otherwise anonymous alley or plaza will make me happy most anywhere.
Add this to an otherwise walk/bike/kayak-able network of streets and canals, and suddenly it seems easy to understand why I enjoyed it so much!