If you took out a brand new $200K loan at 6% for 30 years, then paid $3000 on it right away, you'd knock a whole year off the loan. And save $13K in payments.
As Bill says, life insurance is to provide for those you depend on you. Its to replace the loss of your income. Since the usually retirement guideline is that you should take 4% of your next egg out each year if you want it to last forever, you need 25 times your annual salary in cash to replace your paycheck.
OTOH, life insurance death benefits aren't taxable, unlike your paycheck. If you're paying 28% federal, 4% state, and 7.5% FICA & SSI, you're only taking home 60% of your gross pay. So, if you had 60% of 25X, or 15X your annual salary, you could still take the 4% and have the equivalent of your after tax pay. Now, the earnings on the nest egg would be taxable. So, perhaps somewhere in between those two figures.
That assumes two things:
1) There is someone who's totally reliant on your paycheck, and
2) They're going to spend the rest of their life living off the insurance.
If you're young and single, the first doesn't apply. Nobody's dependent on your paycheck, so nobody but you gets hurt if you step in front of a bus. If you retired and living off your nest egg, even if you do have dependents, there's no paycheck to replace. So, in those two cases, you don't really need life insurance, either.
When it matters is if you have a young family, your spouse is staying at home while you work, and you want to provide for them if you bite the big one. Even then, do you want to provide for him or her to live off the live insurance for the rest of your live? If so, then 15X, 20X or even 25X is not the right number. If you're 25 years old now, you would have some expectation of an increasing paycheck for many years to come. The 4% guideline really says take 4% of the nest egg the first year, and then increase the draw by inflation each year. That's not bad, but may not put your spouse where they hoped to be.
More realistically, IMHO, you want to provide your spouse the ability to adapt to the situation. That might mean paying off all your debt, buying a house free and clear, and providing baby setting money while your spouse gets a degree or skill.
Now, the other half of this story is proper savings and spending. If you're not saving at least 10% of your pay, you're slacking off. If you're spending more than you make (i.e., running up credit card bills), you're REALLY slacking off. I don't care if you make $10 an hour or $100 or even more, if you let them, your expenses will ALWAYS be 110% of what you make. If you're like most people, including me, you have to fight that every moment of every day.
So, buy cheap term life insurance, when you need it. If you're staring a family, buy more. Another member made an argument the other day to buy insurance when you're young and healthy to avoid exorbitant rates when you're older or especially if you end up with some nasty disease. I don't entirely buy the idea of buying a product you don't need on the chance that you will need it later and have to pay more, but there's something to consider. If you have a family history of cancer, diabetes, heart disease or the like, maybe buying sooner rather than later is a good idea. But being diligent about controlling the spending and saving is even more important. If you're 50, smoke and have had a heart attack you're going to pay through the nose for life insurance. If you have a $1 million nest egg (a reasonable goal), then that life insurance isn't so essential.