Distance: 8 miles round trip, with about 3,000 feet of elevation to the overlook of the Icefield.
The hike to the Harding Icefield is the only real trail in Kenai Fjords National Park, but what a trail it is! This is one of my favorite hikes in Alaska, and even if you're staying in Anchorage it's well worth driving the 120 miles or so to the park just for this hike. The drive is scenic in its own right. The upper reaches of the trail are covered in snow for much of the summer (certainly in late July when I did the hike), but the route is well marked and popular enough that this doesn't pose any particular problems - the trail is slippery in places but can be tackled without special equipment.
The trail starts at the Visitor Center near the terminus of the Exit Glacier - like so many glaciers in rapid retreat - and climbs along the side of the valley above the glacier to reach its source at the Harding Icefield. The trail is well constructed but indisputably steep, especially for the first mile and a half or so that it takes to climb above the tree line. Good views start at the 1.3 mile mark at Marmot Meadows where, on the day we did the hike, one of the eponymous critters was contentedly basking on a rock just by the trail. From there, the trail ascends to the Top of the Cliffs overlook at 2.3 miles - from where the panoramic vista of the Exit Glacier above was taken - before continuing somewhat less steeply to an emergency shelter and the icefield overlook that marks the end of the hike. An icefield makes a difficult photographic subject - a sheet of white nothingness - but when you're there in person the views of the glacier, together with the panorama of peaks in the coastal mountains and the icefield itself stretching off into the distance, are extraordinary.
Distance: 8 miles round trip, with about 2,000 feet of elevation to the pass
The Crow Pass trailhead is already at moderate elevation, and it takes only a short time to clear the trees and emerge onto the slopes of the Crow Creek valley. From there, it's a basically straight route up the valley to reach the pass at its head. There are a couple of different trails, a lower route that passes some old mining detritus and a small waterfall, and a slightly easier route that cuts higher along the east side of the valley. The junctions are easy to miss, but as long as the creek above the waterfall is easy to cross (as it was for us, doing the trail in mid-July) it doesn't really matter which route you take. Reaching Crystal Lake at the head of the valley, the climbing is over, and the trail continues gently over the pass to reach the Raven Glacier and a view down along Raven Creek toward the Eagle River valley.
We did this hike on a damp and overcast July day, which did nothing to lessen its scenic attraction (in fact, the low cloud and swirling mist made for a magical scene resembling nothing so much as the Lord of the Rings). It was, however, cold at the pass and the glacier! Take plenty of layers...
Backpacking option: The trail continues past the Raven Glacier, descending the Raven Creek and Eagle River drainages to emerge at the Eagle River Nature Center north of Anchorage. The shuttle backpack is about 26 miles, requires one unbridged stream crossing, and involves less climbing if you start from the Crow Pass trailhead end.
Distance: 9 miles round trip to the ridge, though it's possible to continue further to the South Summit of Pioneer Peak. The trail is dotted with a number of picnic table but make no mistake - it's steep! It's about 5000 feet of climbing to reach the ridge and the best views, from where the panorama below was taken.
Note: from the map it's clear that an even better view of the Knik glacier would be possible if you could climb either Knik mountain or Hale-Bopp peak starting further along the valley. The road goes far enough and the climbs are said to be straightforward once you get above treeline. Access though is tricky - the land in the valley is privately owned, some of it (apparently) by survivalist types not keen on visitors.
Distance: 7-8 miles roundtrip to East Twin Pass, with about 3500 feet of elevation gain.
If you have (or rent) a bike, an alternative is the Bold Peak hike, which leaves from a trailhead about 5 miles down the lakeshore trail. The trail is of similar difficulty to the East Twin Pass trail (about 7 miles roundtrip from the lake, with 3500 feet of climbing, and although I haven't done it I suspect it offers even better views.
Distance: About 4 miles roundtrip to the lake. The trail to the pass is moderately steep but well maintained, whereas the trail down to the lake is steeper and (when we did this, way back in 2008) showed no sign of having seen a trail crew in many a year.
The Eagle River Valley is quite attractive and there are a variety of short loop hikes you can do close to the Nature Center. We saw a woodpecker here, and later in the season bears congregate to fish along the river, so there's a chance of seeing wildlife. You can hike as far as you want along the valley but it's miles of rather tedious trudging through trees before you get to the best views. If you want to see the glaciers at the head of the valley, you're better off starting at the other end of the old Iditarod trail and ascending to Crow Pass.
Distance: it's just one mile on a fairly steep trail to reach the ridge above the visitor center. It's then possible to walk for miles on informal trails (or simply across the open alpine area) in either direction along the ridge.
The interior of Denali National Park is often described as being trail-less but it's not really true - there's a formal trail up to the ridge above the Eielson visitor center and other places where informal but clear routes exist. Eielson is about as close to Mount McKinley as you can get along the park road, and from the visitor center or from the ridge the view of the mountain is incredible. When I did this hike low clouds obscured the view from the visitor center, making the appearance of the mountain as we reached the ridge all the more dramatic. The formal trail ends at the ridgeline, but it's easy to hike in either direction along the ridge and it would be quite possible to spend half a day (about all the time one has given the bus schedules) doing so. One should be aware that the mountain is frequently lost in clouds (we saw McKinley for all of about 3 hours in 4 days spent in the vicinity), so I'd advise spending some days in Denali to at least give you a fair chance of getting a view.
The bus system in Denali is simply excellent (and given the state of the road, you might not want to drive it yourself even if it were allowed!) and you can get on and off the shuttle buses almost anywhere to go for a hike. Much of the terrain - for example along the Toklat valley and near Thorofare pass - is invitingly open, and the only significant impediment to hiking is the difficulty of crossing streams. If I return to Denali, cross country hiking will be at the top of my priority list.
Seeing wildlife is a prime attraction of visiting Alaska, but can be a concern when out hiking. Although I've not seen a brown bear from the trail, there are few if any Alaskan hikes where a bear encounter is not possible. We've followed the standard advice which is to make plenty of noise, especially when visibility is limited, and carried bear spray. You'll also see locals carrying guns, which is pretty normal in Alaska but initially surprising if you're from Europe! If, on the other hand, you want to see bears I'd recommend either the bus tours in Denali, or visiting one of the managed bear viewing sites. The video below shows a visit I made to Pack Creek, flying by float plane from Juneau. It was great fun!
Denali National Park - start here when booking shuttle bus trips
Alaska hike search - this listing of hikes has great local information, though I'm not sure how actively it's updated
55 Ways to the Wilderness in Southcentral Alaska - we found this to be the most useful hiking guide
Great photos from our 2008 trip to Anchorage and Denali, and our 2012 visit to Anchorage and Juneau, from my brother