I agree that certain types of debt are better paid off as slowly as possible. I make that case for mortgages here. The gist is that the combination of low rates, deductibility of the interest on balances up to $750k, and the long term effects of inflation mean that in some cases you may end up making money on such loans. As I explain in the article, it’s also safer to invest extra cash than prepay your principal.
In response to Greg below, the difference between that and borrowing money to place in the stock market (a.k.a. investing on margin) is that mortgages are used to buy a home, so you’re not borrowing simply to get the spread.