This is another driving expedition right in your backyard, that just about anyone crazy enough can undertake. It is probably best done from the West Coast. In fact, I read about a group of VW bus enthusiasts who rallied together in Vancouver and headed for Inuvik. They didn't get as far as Tuktoyaktuk, though.
There are a couple of different routes you can take through British Columbia. By the time you hit the Yukon Territories, it is going to be Route 1, than the Klondike Highway until just outside of Dawson. The you can take the Dempster Highway all the way to Inuvik. Check your map.
Now the best part... if you've managed to get this far during the winter months, you can actually, legally, DRIVE THE ICE ROAD, just like in Ice Road Truckers, to Tuktoyaktuk, located on the shores of the Arctic Ocean, at the very top of the world. Best of all, unlike the sissies driving actual "roads" to Prudhoe Bay in Alaska, you'll have traversed a frozen river and a frozen bit of the OCEAN for 150 kilometers.