Save or pay off loans?

I was lucky enough to get out of college and graduate school with no debts to speak of. This is almost entirely due to the scholarship I had as well as good spending habits and a relatively inexpensive lifestyle.

My previous post Save first, then spend said that you should automatically divert some portion (10%) of your incoming money to an account you will not frequently see (and therefore will not think you are able to spend the money). I'd like some feedback from those with student loans (or other debts) they are paying off. Do you save money or immediately try to pay off the loans any way you can? Is the save first strategy a good one for someone with debts?