Depends where you are in Copenhagen, but there's lots of options.
Taphouse is quite central, and has lots of taps!
In Vestboro you have:
Warpigs - Brewpub run by 3 Floyds and Mikkeller, also great BBQ food there, so maybe go for lunch)
Fermentoren - Pub run by Dry and Bitter brewery.
In Nordboro there is:
Himmeriget (smaller bar, but nice)
Brus (lots of stuff brewed on site)
Mikkeller & Friends (run by Mikkeller)
All of these have a big range of beers - hoppy, dark, sour, lagery, fruity or a mix! It's all eyewateringly expensive, so unless you've got an expenses account order the small beers (200ml), take your time and try lots of stuff.