My mother-in-law has a 10 year visitor's visa for the US. Her passport will expire next year before she plans on visiting us again. There will still be 5 more years left on the visa. After she gets a new Thai passport, will she have to go to the US embassy and have the visa transferred to the new passport or can she simply show the visa from her expired passport?

See Frequently Asked Questions About Nonimmigrant Visas:

Q: I have a valid United States visa in an expired (old) passport. Can it still be used?

A: Yes, if you will be entering the United States for a reason consistent with the type of valid visa you have. You should carry the old passport that contains the valid visa and your current (new) passport. You will use both for entry to the United States.

Also from Most Frequently Asked Questions:

I have renewed my expired passport which contains a valid U.S. visa. Can I still use the visa?

If the passport in which your visa has been endorsed has expired, the visa in the old passport still can be used provided that you also carry a valid passport of the same nationality. If, however, the passport authority clipped the corners of the passport when canceling your old passport and, in so doing damaged the visa in any way, that visa is no longer valid and cannot be used for travel. In such circumstances you will be required to apply for a new visa, or if eligible, may travel visa free under the Visa Waiver Program.