Miles With Free (or Almost Free) Change & Cancellation Fees

There are lots of obvious reasons why miles are better than cash, like the ability they give us to book mini palaces on planes that look like this...

Etihad First Class Apartment on an A380

...or the loose routing/stopover/open jaw rules of some programs that allow us to see more places on one trip.

But what about the smaller perks we often overlook? Like free or nearly free change and cancellation fees?