It probably does make sense for you to buy term life insurance separate from your employer, for a few reasons:
- If you lose your job, you won't have the coverage.
- It probably doesn't give you as much coverage as you need. In my experience, you only get 1 year's salary from your employer, which may not be enough depending on your goals.
- If you are allowed to pay to continue the policy after getting laid off, your premium will probably be much higher than you'd get from an agent. (Assuming you're in good health.)
- The policy you have through your employer may not cover all situations. A term life policy you purchase may have broader coverage. Read the policy from your employer carefully to see what it excludes.
There are a number of life insurance calculators on the web. Try two or three -- some of them ask different questions and can give you a range of answers regarding how much coverage you should have.
Then take a look at some of the online quote sites -- there are a couple that don't require you to enter your personal information, just general age/health/zip code so you can get an accurate quote for a couple of different coverage levels without having to deal with a salesman yet. (It was my experience that these quotes were very close -- within $20/year -- of what I was quoted through an agent.) Using this information, decide how much coverage you need and can afford.
If you're a homeowner, and the insurance company with whom you have your homeowner's policy offers life insurance, call them up and get a quote. They may be able to give you a discount because of your existing relationship; sanity check this against what you got from the quotes website.