You will probably reach a point in your savings and debt elimination goals where you will have a hefty amount of money tucked away in your savings. It gives you confidence just thinking about it.
Then you look at your loan or credit card or other debt balance and the feeling starts to dissipate. The next thing you know, you're contemplating dumping your entire savings into that debt balance so you can either get rid of it all or a chunk and pay less interest over the long haul.
I'll say this now, what happens if the next day your car breaks down or you need to fly across the country to see a dying relative or disaster strikes and you need to move? Anything can happen and if you dig into your savings to pay off debt, you'll position yourself to easily get right back in the whole you've been digging yourself out of.
Keep your savings for what its for. You can always pay extra to your debtors when you have extra.