Copenhagen has a card. Stockholm has a card. And Helsinki has a card.
The Copenhagen Card (or, as they display it, the cOPENhagen CARD; I'm guessing this clever typography only works in English), the Stockholm Card, and the Helsinki Card all provide the same thing: free or discounted transportation and admission to tours, museums, and other attractions.
I could have bought my Copenhagen Card at the airport when I arrive, but I figured it's worthwhile to have it with me so it'll be one less hassle to deal with. I can use it immediately to get from the airport to where I'm staying. I bought a 72-hour card for about $90. I could have just bought a 72-hour CityPass for the metro; that would've been about $33. (Single tickets on metro are about $4.25.) But I figure I'll visit a few museums and do other stuff that'll make the pass worthwhile. Admission to Tivoli Gardens is free with the card, otherwise $17. Saving should add up quickly.
The Stockholm Card provides a discount for ordering it online, and they have the option of picking it up at the tourist bureau (across from the train station) on arrival, but I'll be arriving on Sunday evening, and they close at 16:00 on Sundays. So I ordered a 5-day card for $139. Again, I could've bought a metro-only pass for about $48, but I'm sure I'll do other stuff that the Stockholm Card will be good for.
The Helsinki Card is the least expensive, and also probably the one I'm least likely to need. I'm arriving by ferry, and the terminal is within walking distance of the hotel, so I won't need it when I arrive. If I do decide to get one, I can buy it at the hotel. A 3-day card is 56 euros ($74).
So... three weeks from today, the adventure begins!