The Copenhagen Card is Copenhagen's official "city card," which gives you access to over 80 attractions in the greater Copenhagen area.
If you plan to visit a lot of "attractions" included on the Copenhagen Card, then it can be a great deal (and just simplify your visit) since it also includes public transportation. I would use the "Savings Calculator" tool on their website after you've planned your itinerary to help you decide if it would be worthwhile or not. For what it's worth, my family got the Copenhagen Cards the first time they visited Copenhagen and were really happy with them! On subsequent visits, we didn't do as much "touristy stuff" so they haven't bought the cards again.
The Lykke Charm Guide to Copenhagen
Copenhagen, Denmark
Go check out my guide for the best free things to do as well as itineraries and travel tips to make your trip unforgettable.