I paid off my rental condominium several years ago, and have been steadily (annually) nagged by my CPA to get into more mortgage debt for the tax write-off. I do have a small HELOC on the property, and have to exercise control to keep from the temptation of freely spending the available credit line on whims..like Lincolns and Miele appliances. A HELOC is nothing more than a gentle term for a second mortgage.
The "free money" rental income is quite nice, though, although like everything else in life, there are property taxes and up-keep on the place. I'm all about keeping my long-term tenant happy so she'll stay put.
What would make the most sense is to plow the money into our remaining (12 year) mortgage on our house or paying off the Prius early. Right now, some of it's going into retirement savings, as that will be facing me in 20 years, and I want to be ready...or as ready as one can be in this economy.