I would have to agree. You definitely should have a cutting instrument readily available, but it need not typically be very large - something on the order of a Swiss Army Tinker or one of the Leatherman tools has worked for me on numerous occasions in a variety of circumstances. On one trip in Oaxaca a few years ago, like every other sentient male in the vicinity, I carried a machete and found it useful, so yes, indeed, environment and circumstances should influence what you humparound.

What have I most often wished I had carried that I did not have at hand? Either more water, a bit more climbing rope, or on occasion, another insulating layer. Size up the situation and adjust your equipment.