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My employer offers discounted life insurance as an employee benefit. I pay $70 per year for about $200,000 of coverage. Buying comparable coverage outside of work would cost me about $300-$400 per year at my current age/health status.

I understand that if I leave the company for any reason, such as taking a new job or being fired or laid off, I instantly lose this life insurance. Additionally, the older or sicker I am, the harder and more expensive it would be to get affordable life insurance.

I have a spouse who currently works and kids under age 10. Is there a strong case for purchasing my own term life policy in addition to (or instead of) what my employer offers?

The rule of thumb for life insurance is to have 10 times your income if you have people that depend on your income. 10 times let your beneficiary invest the insurance at relatively safe return levels and will last many years. With kids under 10, $200K is probably not enough to support them if you pass.

Shop around for 10- or 15-year term insurance to get you closer to 10X your salary. After 10 or 15 years, you can reassess your needs based on if kids are still dependent on you, and how much retirement savings you have (which can be used in place of life insurance).

Don't mess with whole or universal. They are typically sold as investments combined with insurance, but the amount you pay above what equivalent term insurance costs usually has a bad return as an investment.

If you think your current life insurance coverage is not sufficient, you buy additional term life insurance. There is no reason replace your employment benefit with a a higher rate for the same insurance benefit. If your employment situation changes, you are always free to buy term insurance then.

In addition to the recommendations by DStanley, consider getting a term life mortgage insurance policy if you own a home with your spouse as the beneficiary. These policies have a level premium for n years (typically 15 to 30 years) and a death benefit that reduces approximately as the remaining mortgage balance declines over the n years. Once upon a time, and perhaps even now, typical mortgages had clauses to the effect that in case of any changes in the financial situation of the family (e.g. the primary breadwinner dying) that would cause the lender jitters, the principal would be due immediately. So, having a mortgage insurance policy ensures that the grieving surviving spouse has one fewer matter to be hassled about. Besides, not having a monthly mortgage payment anymore is effectively additional disposable income for your spouse.

Note that this policy is different from the quite expensive policy that a lender will sell you (or even insist upon selling you if your downpayment was smaller than what the lender considers adequate) for which the beneficiary is the lender, and if you have been making extra payments towards your mortgage, the lender will make a little extra profit off of you.