For the past 4 summers, my extremely fit (now 14 year old) son and I take a major trip together. Last summer, we flew to California from Montreal and toured the state. Sight seeing does not interest him very much. After 5 minutes, he says "yea, yea yea, another tree, mountain....". He is into adrenalin activities. Last summer, we climbed Half Dome in Yosemite, we went spelunking the last 2 years, white water rafting last year, zip lining, waterparks, Zorbing, etc... We both look forward to these trips every year. Spelunking was his favourite activity (what son wouldn't like to see his dad trying to fit through a small crack deep underground...only to get stuck). I'm currently planning next summer's trip and I'm torn between 2 geographies. I'm thinking about western Canada and USA (Yellowstone, Glacier National Park, Seattle, Vancouver Island, Vancouver, Rockies and Banff) and Scandinavia as possible destinations. The latter appeals to my sense of adventure but I'm struggling to find adrenalin activities for both of us. We are both adventurous and nothing is off the table. Do you have any recommendations? Neither one of us is into history or visiting churches. While we don't mind it, our goal is always the same, to be very active and have lots of fun.
Come on out West and go Sea Kayaking! Puget Sound, the San Juans and the Gulf Islands as well as the Inside Passage have water trails. They have guides and lessons if you haven't been in a Kayak. A lot of BC and Alberta is still Wilderness as well as the North Cascades in my State. I have friends that have been to Scandinavia recently and they said everything was very expensive.
Probably not what you had in mind, but if you're in Copenhagen, you might want to visit Tivoli Gardens. I know it sounds like a touristy thing to do with little kids, but it's a beautiful place with some great roller coasters, including the oldest working roller coaster in the world. You'll find good food, too. It's right across from the train station, too, so it's easy to access.
I cannot believe I am saying this, but - Pacific Northwest. We've got it all, from sea kayaking and whale watching to mountain climbing, camping, hiking, zip lining, bungee jumping (heck - base jumping!), heli-skiing, adventure racing, white water rafting and yes, spelunking.
The area is unbelievably gorgeous. The possibilities are endless. You could spend the entire vacation moving from adventure to adventure and never set foot in a church or a museum. And it will cost less than the equivalent fun in Scandinavia, I am thinking.
Some links to get you started:
http://speleo.us/gallery/Pacific_NW_Lava_Caves
http://outdooradventurecenter.com/
http://www.trioba.com/
http://www.parks.wa.gov/yurtsandcabins/
http://www.kayakbc.com/
http://www.kayakingtours.com/
http://www.hellobc.com/british-columbia/things-to-do/outdoor-activities.aspx
http://www.hellobc.com/british-columbia/things-to-do/outdoor-activities/ziplining-bungee-jumping.aspx
Another thought... Iceland has a ton of outdoor adventure things to do, if you decide on Scandinavia. Icelandair is running a great special where you can stay up to 7 days and not pay anything additional for your eventual connecting flight.
Since you mentioned Scandinavia, a number of years ago we went camping in Finland. There are lots of ferries running in the islands between Finland and Sweden. We were in a car but there were tons of people on bikes with camping gear. We stopped and camped on several islands. Great camp grounds with kitchen facilities. We were there during the summer solstice so it was light until midnight. Mosquitoes were a bit challenging so a tent was essential. Lots of kayaking, saunas and jumping into the sea. Some maritime sites and a museum as I recall.