"Do you own or rent your home?"

Renting or owning a home sometimes indicates your financial status. Renters are usually people who do not have enough down payment for a house or people with bad credit who cannot get a loan. So it is best to have your own home, but if you don't, then give them an answer that shows you are preparing to buy a home.

"I'm currently renting, but I plan on buying my own place next year."

"I'm renting right now, but I'll probably buy a house when I get married."

If you own your house, then a simple, "I own my house." will be a good enough answer.