An anecdote:

I had written most of a program to generate a big SQL import script when I realized that I actually needed some data I had stored in hashes to retain its order. I could have changed my code to use an array as well as a hash, but instead I just replaced the hashes with Tie::IxHash and everything just worked, with no other code changes. That was beautiful.

I usually avoid using tied hashes because they are slower than just calling object methods, but in this case it was really handy.