This is also my favorite type of fishing. I normally hike several miles in and usually end up doing several miles of stream fishing. I generally fish small creeks and therefore do not do much wading; only stream crossings, and minor wet wading, so as to maintain stealth. I just wear my Goretex waterproofed hiking boots and bring extra wool sox in my pack to change into for the hike back up the trail. Zip-off hiking pants are great too in Summer. I have one of those anglers backpacks (Cabela's) which is perfect for me. I carry all necessities, light fishing gear, packable rain gear, lunch, snacks, maps, etc. in it. My 5-piece pack fly rod fits in a tube which straps right to the pack. I carry a folding wading staff which I use as a hiking staff.
I have often wondered how light (and small) packable waders and/or hip boots are. Guess I should look at them next time at a flyshop.....
The best part is that even if the fishing isn't very good, at least you have been hiking.
For a real challenge, try ice fishing with dry flies.