You know, there has been so much written on this topic that I feel foolish to try to recapture what has been said by better women and men than me. That being said, I see no reason why ANY pilot with a private pilots license and some experience working within the US ATC system can not easily make the flight up through Canada and all over the state of Alaska if they keep a few things in mind.
Canada is different. It is just similar enough that if a pilot flew all the way through Canada, using the same procedures used in the US he would probably be fine, but it is still different. Everything you need to know is contained in the AOPA web pages dedicated to Canadian flying, and in the
Canadian Flight Supplement. Actually, if you read the Canadian Flight Supplement from cover to cover, omitting the airport information from the hundreds of airports that you don't plan to visit, you will be an expert in negotiating Canada's airspace and do very well. That's what I did the first time
You will become intimately familiar with the use of 126.7. You will understand what a upwind midfield entry to the traffic pattern is and why it is important. If you don't do it already, you will learn to file and activate a VFR flight plan for EVERY flight, and learn that Canada will automatically open your flight plan upon takeoff and close your flight plan for you upon landing assuming the airport is manned. You will learn the difference between "radio", "twr", and "MF" radio frequencies listed in the airport directory and Jepp database and why they are often the same frequency at a given airport (and don't forget to add "november" to your radio call sign there e.g. "Cessna november 3477 charlie.")
If you read the stuff on AOPA or others' trip reports you will learn why pilots who have grand plans for flying IFR for some part of their trip up here soon abandon that plan somewhere north of Edmonton. Why having some mountain flying experience is a plus but if you are conservative on weather, fuel and judgment in general you will be perfectly safe flying through the mountains on the way up here for the first time. You will read how building a few days into your trip each direction is smart considering you might likely be sitting around waiting for ceilings to lift in a few key squeeze points (usually Teslin to Whitehorse somewhere.)
For flying in Alaska, it is much of the same as the lower 48. It is still the FAA running things up here, even more so really. It's hard to articulate the differences
Good rule of thumb is try to stay UNDER whatever is blocking your way - be it weather, MOAs etc. Most of the flight corridors from Whitehorse to Fairbanks or Anchorage and in-between exist in broad valleys between mountain ranges or hills, which tend to trap moisture layers. No problem, but just stay UNDER the layers. Don't get sucked into complacently and fly VFR over the top unless you are flying something with long range and fast speed and are sure of the CAVU conditions at your destination - I for one always take the time to stop and spiral down to get under whatever layer appears before me. Get used to flying low and slow like the natives, no one flies more than two or three thousand feet AGL around here, and usually it is more like one thousand AGL. IFR means "I follow the road" here, because for the typical tourist pilot routes in my part of the state you will be following valleys which have highways in them anyway, and they present great emergency landing strips if you have a problem. There is no reasonable flight following here, you are just too low for radar coverage in most spots. File a flight plan! I do choose to avail myself of approach services at both Fairbanks and Anchorage though neither are required - too many little airplanes flying around!
The Alaska Range tends to divide weather systems and so the passes can be quite windy as pressure gradients try to equalize, though this is much less common in summer time. It is usually very pleasant flying weather here in the summer. From Northway west to Fairbanks and south to Talkeetna and Willow we are subject to afternoon thunderstorms which can be quite spectacular, so if you are here flying in the warm months the rule of thumb about trying to accomplish most/all of your flying in the morning often applies.
What hurts visiting pilots here: flying above/between/into clouds. Trying to fly through obscured passes. Flying into box canyons. Circling moose/caribou/whatever and stalling. Exceeding their abilities and trying a little off-airport or short strip work without ever having tried it before.
Flying into the Anchorage area can be challenging both in terms of traffic and procedures. If you are used to flying in a busy class C or B it will be no problem but requires advance research on the special procedures airspace. Fairbanks is easy peasy, class D with TRSA. Pretty much everywhere else is uncontrolled, though many airports (here as well as in Canada) actually still have a FSS on the field actively providing airport advisories. You will need the Alaska supplement, and don't forget to look in the sections regarding special procedures to see if any exist for the airport you are flying into.
What else do you want to know, I'm rambling here
I flew my plane up here from near Edmonton to Fairbanks during the month of December with less than 150 hours total time in my logbook, some good previous mountain flying experience from the desert and a pretty fresh tailwheel endorsement.
I managed not to kill myself and had one of the classic experiences of a lifetime.
Thanks Richard!!
Taking a co-pilot makes it a much better trip.
Also check out my approach into Fort Nelson 
Now all I have to do is wait for them to call me back. 
