Summer is peak season, with the major population influx coinciding with the end of the school year and the beginning of the salmon runs. Long daylight hours make it easy to burn the candle at both ends. Some of this can be avoided by using the shoulder seasons, but spring and fall can be a bit iffy, weather-wise. Autumn starts early here with the tundra plants and the deciduous trees beginning to show color in mid-August. The animals are actively getting ready for winter, there are plenty of fish to catch, and most of the visitor services stay open into September.
We like to recommend no fewer than two weeks, three being a much better option. That'll give you time to hit the hot spots: see Kenai Fjords and/or Prince William Sound, Denali, the Kenai, and points in between without turning the trip into a test of endurance. It goes without saying that even just five days here can be sublime.
Carry a day pack with an extra layer (or two) of clothing including rain gear, water, and snacks as a bare minimum. Everyone should have his or her own pair of binoculars, even if it's just an inexpensive set. There are few things more frustrating than having the wildlife sighting of a lifetime with everyone grabbing for the same set of field glasses.