+1 on the Sven saw; reasonably light and effective. I have used one on SAR operations, usually when we had to whack out a helispot or clear a trail for a litter.

But for normal recreational backpacking? Little if any need for a saw. I do have a saw blade on my Leatherman Wave, and I have used it for tasks like preparing a hiking staff. That is about all you need for recreational use, and even then it is not critical gear.