I'm generally a Dave Ramsey follower, and I agree with his idea of paying off the lowest balance off first for several reasons.
That said, mathematically Weezl is 100% correct on this. Every single time, you will pay less in interest if you pay off the highest interest rate first. There is no arguing against this, as it's just simple math. Dig around enough on DR's info and he clearly discusses this. It's not up for debate, just facts and math. If you want to look at the numbers, try this spreadsheet. It will let you put in all your debts and look at various scenarios to see the differences when you pay off things in different sequences.
The reason I subscribe to paying off low balances first is that it frees up income sooner and it lets you psychologically feel real progress as you eliminate debts. Each one you eliminate lets you push that income to the next debt. If you're paying off smaller items, then you quickly have 'extra' income that is available if you suddenly have a short month. If you're talking about a car loan with a high interest rate and several years to pay it off, you may have knocked out half of it but you're still stuck paying the full amount in a month that you have an unexpected bill and the amount you've paid off doesn't come back to help you out unless you've completely knocked out the bill. Hope that makes sense, I'm not sure I worded it very clearly.
yes, this is exactly what i was trying to say, but didn't really feel like putting enough thought into wording it that way...
adsm, i think what you're trying to say i agree with also... if you have 3 credit cards with interest rates of near identical values (say .1 % difference or such) then i would pay off lowest balance first, that makes sense