How long does it actually take to pay off a house?

Really depends on whether you make additional payments beyond what are required. Paying 1 extra payment per year on a 30 year loan will pay it off about 7 years sooner; paying 1/12 extra each month will do roughly the same. Otherwise, a 30 year loan will be paid off in 30 years; a 15 year loan will be paid off in 15.