There are a variety of "answers" to this question in my experience. Some answers from my experience:
I was wearing a great kilt for a Halloween community service event. A female friend comes over and asks, "Hey Art, What's under your kilt?" I say, in my best Scottish accent, "Well, lass, if you give me your hand..." She actually proceeds to do so, and I place it on the inside of my right knee and very slowly slide it up my thigh under the kilt. About, oh, 3 inches from the top, I managed to finally call her bluff.
A different female friend, about a year later. Once again, I've put on my great kilt. She asks me, "Art, are you regimental?" I say, "See for yourself." She goes to lift the kilt and everyone goes silent. We decide that she should actually do the lifting elsewhere. For the curious, I was in fact regimental at the time, and no, she wasn't bluffing.
Then, of course, there's the jokes involving this line. One of my favorites, the punchline of which I've used when asked this question:
A Scotsman is walking down the street when a woman in a convertible pulls up along side him. "Hey Scotty, what's worn under the kilt?"
The Scotsman turns and asks, "Lass, do you really want to know?"
"Sure I do!" she says.
He walks over right up next to the door to the car and says, "You sure you want to know, lass?"
She feels a little scared but isn't about to back down, and replies, "Yes, I do."
The Scotsman says, "Why, nothing's worn under the kilt, lass, everything's in perfect working order."
A final answer to the question posed in the node title: "Shoes and socks."