There’s a popular recent Subaru commercial that opens with a family of dogs driving down a suburban street. Dad, a golden retriever, pulls up to a stop sign; mom, a labrador, is in the passenger seat.

The poodle is one of the oldest known breeds, once used as game retrievers and truffle trackers. Whether it’s the standard, miniature or toy, on Poodle Day we celebrate the smart, sharp and regal dog ...