Interest payments on your original mortgage - assuming the mortgage isn't larger than the purchase price of the home - are fully deductible for most homeowners. That's a key reason why homeownership is a superb tax shelter. Mortgage interest on a second home is also deductible, as explained the "Vacation Homes"  forum.
If you own a third home for personal purposes, the mortgage interested is treated as "consumer loan" interest and is not deductible. Interest on home equity loans (see "Equity Loans" section" is deductible" with some limitations.