Camping near a guy with a machete: Never. (This as a result of an encounter with a fellow with slightly glazed-over eyes and a tightly-sealed tent in July, who asked us a couple of questions about gear before exclaiming, "This machete is AWESOME!" as he half-staggered toward his next tree-victim. We decided to hike a couple more miles before camping.)
Axe: Not for the last 25 years or so. I carried a small one in my early camping days, when I used cooking fires. However, after I got my first non-Sterno stove, I retired the axe; a few years later, when I realized that fires are way too much like a chore, I quit lighting fires, too.
Having said that, I'll also add that I do not do any bushwhacking or trail work; I stick to traveled trails in the Eastern US. If I did a lot of off-trail hiking, or was hiking in an area that I knew was overgrown, or was helping to establish a trail, I could see where an axe or machete could come in handy. Of course, if everyone who went off-trail used one freely...
But for recreational backpacking, I never feel anything close to the need for either.
Edited by Glenn (01/08/10 02:14 PM)