On my trip to Alaska, the only reservations I made ahead of time were for Lake Louise and Denali NP Tek campground. Lake Louise was a few days ahead of time, and I was pretty fortunate to get it as it had rather obviously been a cancellation: it was the only site available anywhere near Banff for quite a span of time. Denali was maybe a week and a half in advance and was getting towards filling up when I made it.
The only places I had any hint of trouble finding a site besides these were Jasper (stayed in overflow camping, which has a great deal of space but limited privacy and amenities) and once in Fairbanks (wanted a place with an RV wash after going over the Dalton Highway), and Dawson City (happened to get there when a music festival was in town, sites were very nearly gone when I got one in town).
In general, you don't have to go a long time in advance, and rarely at all in advance if you're a little bit flexible. I'm not sure how many of the provincial or state parks accept reservations; it's certainly not all of them.
If you don't have a copy, I heartily recommend Churchs' book ("Traveller's Guide to Alaskan Camping") which I found very complete and well-organized and unusually good reading for a campground guidebook.