The best term life policy for you will depend on your personal financial history, current progress and outlook. Since term is the most basic type of life insurance, there aren't as many varieties of policies as there are with whole life. However, a typical term life insurance policy can provide you with short-term (well, up to 30 years in most cases) financial protection that allows you to achieve temporary goals such as paying off a mortgage or getting rid of pesky high-interest debts.
If you happen to die while your term policy is still in effect, the amount specified on the policy as your death benefit will be paid to your beneficiaries (the loved ones you designate). If you outlive the policy, you don't receive any benefits, but you can renew the coverage - for a higher premium cost. In fact, every time you renew a term policy, it grows more expensive, eventually becoming more costly than many permanent life policies. Therefore, term insurance is usually a better deal only for the young and those with a specific temporary need for insurance.
There are companies (like Prudential or MetLife) that offer 20-year term policies that have somewhat flexible plans. For example, the premiums may stay the same for 10 years and then be higher (but still level) over the final 10 years of the policy. There are also increasing premium term policies that offer temporary protection at a low starting rate. You can renew such policies each year without having to prove that your health is good.
Finally, there are term policies that go up to a certain age, for example, age 80. The premiums can stay the same for ten years and then increase year by year. Hopefully you can sort out your insurance options easily!