Trott-Strzebonski method for In-Place Evaluation

One of the all-time cleverest idioms I've seen; this was discovered by Michael Trott and Adam Strzebonski a few years ago.  The template is a rule of the following form:

   lhs :> With[{eval = lhs}, eval /; True]

Suppose you want to replace a bunch of things inside a held expression, and have the replacements evaluate.  You don't want to evaluate the whole, just the pieces that are targeted.

You can also do this with ReplacePart, but it's harder to code, and has a worse time and space complexity for a large number of substitutions (and using Fold with ReplacePart would be O(n^2)).