I'm never sure how to answer the question. A couple of times I have responded, "A naughty one," because Lucy at that point in time was dancing on her hind legs, straining to hug her new friend and hoping for a treat. That was cute at six months, not so cute at 70+ pounds.
Now I usually answer, "A mutt. The vet thinks maybe shepherd and Akita."
The reason for their curiosity puzzles me. Since Lucy doesn't really look like any particular breed I've seen, I assume that she looks like a mutt to others as well. However, everyone who has met her claims that she is a beautiful dog, which of course she is. She is gorgeous in her muttiness. I wonder if people assume that such an attractive animal must necessarily come with a pedigree.