No, as a US citizen, you can stay in 26 European member countries of the Schengen Area without having to apply for or obtain a visa for up to 90 days for tourism or business during any 180-day period. You'll need a valid U.S. passport, and remember not to overstay. Starting from November 2023, US citizens will have to also apply for an ETIAS before traveling to Europe, in order to be allowed to enter Schengen countries.