It depends entirely what the interest rates are for the loans. Think if paying off debt as a long term investment at the loans rate. If you could get (for example) 5% by leaving it in a savings account you would be better off (long term) to pay the loans if they have a >5% interest rate (like a car loan) but you are better off leaving it in savings if it is <5% (like a student loan) on the loan.
I financed my condo using an 80/10 loan. The interest rate on the 10 part of the loan is fairly high, 8.75%. I'm dumping as much money into that as I can to try to get it paid off this year because that's currently one of the best investment opportunities I have. I'm not getting that kind of return on the stock market, my 401k or my savings account, that's for sure. The major problem with this is that it's a very illiquid form of investment. Once the money is paid into the loan it is hard to get back out if you need it.
People also tend to fall into the trap of telling themselves "well I'm now debt free, so I can take on more unnecessary debt." If you just paid off the loan on your 2 year old car, don't go right back out and buy a new one because you can "afford" it because you have no debt.