If my spouse dies, do I still get his/her Social Security?

Yes; you will be covered under the Social Security Survivor's Insurance program. And this being Social Security, there are the usual array of odd rules that determine how big a benefit you will receive.

If you have already reached full retirement age (somewhere between 65 and 67 based on your date of birth; if you aren't sure, check your latest Social Security annual statement), you're entitled to 100% of your deceased spouse's benefit.

If you're at least 60 but not yet at Social Security's definition of "full retirement age," your payout will be somewhere in the range of 71% to 99% of your deceased spouse's full benefit. Note that a widow or widower of any age with a child under age 16 is entitled to a 75% payout.

Find out more about Survivor's Benefits here.