My visitor visa (B-1/B-2) expires after my intended date of arrival in the U.S. Do I need to get a new visa before departure?

You can arrive in the U.S. right up to the last date of validity indicated on the visa. The Customs and Border Protection officer on arrival determines the duration of your stay in the U.S. Your visa can expire while you are still in the U.S. – just be sure that you do not overstay the period of time the officer grants.