No. For the same reason I don't own a lasagna cutter, or a steak cutter, or a sandwich cutter... I find that an ordinary knife and a fork do the job just fine. I seriously didn't know this was really that much of a "thing", and not just a "gimmicky" piece of kitchenware.
I didn't know some people considered pizza cutters to be uppity utensils. I've used a knife when I couldn't find the pizza cutter, but I much prefer the pizza cutter. You can get one for $1 and they're easy to use. I don't really want to waste 45 minutes trying to use a steak knife.
Yes, I definitely own a pizza cutter. Now that I think about it, I've probably been using it for 20 years now (and that's a conservative guess). Cleans easily, and cuts through both thin crust and thick crust pizzas with little effort.