Personally I havent used one. Never owned anything practical for carrying in the bush just for the sake of having it. But there have been times I having one would have been nice.
Ive thrown together a list of some of the options, and some pros/cons. If youve got experiences with any of these, or others share what you did and didnt like about it.
Wire Saw
pros: very light & compact
cons: junk? Les Stroud used one in one episode of survivorman and broke off the ring on the first pull
Chain Saw
pros: light & compact, said to cut quite quickly, could tackle larger diameter material easier than shorter rigid blades
cons: handle mounts possible weak points like wire saw?
Coghlan's Folding Saw
pros: cheap, replacement blades available in practically every town
cons: quality/durability?
Folding Bow Saw
pros: easier to work with
cons: size
Swiss Army Knife/Multi-tool saws
pros: more likely to have it on you, probably already own one
cons: short blade limits usability
Ive thrown together a list of some of the options, and some pros/cons. If youve got experiences with any of these, or others share what you did and didnt like about it.

Wire Saw
pros: very light & compact
cons: junk? Les Stroud used one in one episode of survivorman and broke off the ring on the first pull
Chain Saw
pros: light & compact, said to cut quite quickly, could tackle larger diameter material easier than shorter rigid blades
cons: handle mounts possible weak points like wire saw?
Coghlan's Folding Saw
pros: cheap, replacement blades available in practically every town
cons: quality/durability?

Folding Bow Saw
pros: easier to work with
cons: size

Swiss Army Knife/Multi-tool saws
pros: more likely to have it on you, probably already own one
cons: short blade limits usability