Can anyone recommend a particular kind/type/brand of peeler that can stand up to the squashes of fall?

Any good "Y" peeler will do the job for you. But never underestimate the value of a good sharp knife.

This one, also by kuhn rikon, is my favorite--the serrated teeth cut through everything.
http://www.google.com/products/catalog?q=kuhn+rikon+serrated+peeler&um=1&ie=UTF-8&tbm=shop&cid=10765803769375847381&sa=X&ei=4qyHTtOkMcXw0gHzlJXDDw&ved=0CFIQ8wIwAA

These are my go-to peelers; they're sharp and lightweight. I buy a set every year or two (mostly because ANY peeler is going to dull at some point).

http://www.google.com/products/catalog?q=kuhn+rikon+peeler&oe=utf-8&rls=org.mozilla:en-US:official&client=firefox-a&um=1&ie=UTF-8&tbm=shop&cid=2047990545606388331&sa=X&ei=95aHTv3SJcrq0QGQ4fjZDw&ved=0CIkBEPMCMAE