This is an interesting discussion. Myself, I usually grab a trail map of the area I am hiking on, and when I want to venture off trail, I mark where I was with my GPS so incase I can't find my way back to the trail myself, I will find a clearing (or some area) where the GPS can get signal and get the general direction of the trail and then use my compass to find my way back. Sometimes I will recheck my progress on the GPS.

I think that relying completely on one or the other is down to personal preference, I just can't trust my map reading skills enough to not have a backup plan. Normally, I like to just use a general heading when I leave the trail, such as, I left heading east, so the way back to the trail is west.

I haven't much experience hiking outside of Michigan, but even in pretty dense forest, I have not had a problem getting a GPS signal, although it may take an increased time to get one.