Obviously I would never advise cutting down tress or doing any trail maintenance where that is not allowed.

Corona 10 inch folding saw. I've been carrying a Corona saw around on the trails for years now. This latest one is the best by far. The 10" length lets me cut through some sizable trees and the curved blade really cuts through the wood efficiently.
When the log is too big for that saw above, or too many cuts would be required to affect the ride too much, I usually just end up leaving it, usually within a week, someone with more fortitude has come along and fixed things. Occasionally a log remains on a favorite lesser used trail for longer and then it's up to you to fix it. That's where a sawzall comes in handy. I've found this battery powered ryobi unit fits perfectly in a camelbak hawg with two batteries and an obscenely long blade. I put in some cardboard too so that there weren't any lumps sticking into my back, it works surprisingly well. Here's a picture gallery of how it al fits in.
