Is it better to be 100% debt free or to carry a property loan for the tax writeoff?

I had seen this tip on one of Oprah’s “everyday millionaire” shows—you know, where the couple next door is very wealthy, but you’d never know it because they live just like you? They all said to keep a mortgage so you have something to write off. But since I’m nowhere near “millionaire” status, would that apply to me as well? Or am I better off paying off everything if I can?