Inspired by this quote attributed to Alan Perlis:
For every polynomial-time algorithm you have, there is an exponential algorithm that I would rather run.
How I interpret this statement is that some exponential running times should be preferred over polynomial ones for realistic problem sizes. I have never actually seen such a case though.
I wonder if there are any problems for which exponential algorithms are known that are preferable to the best polynomial ones up to a nontrivial problem sizes?