U.S citizens do not need a visa to visit Sweden if the visit is 90 days or less.
Visa-exemption agreements entered into before 1 September 1993:
Sweden has entered into visa-exemption agreements with a number of countries prior to 1 September 1993, and these agreements remain effective. Citizens in the countries below may, due to provisions in the Schengen regulations, travel to and stay in the Nordic countries for three months regardless of whether they have previously stayed in another non-Nordic Schengen country. A stay in another Nordic country during the last six months will be counted as part of the time period of residence permit exemption. A citizen of the USA who has stayed in France for 90 days may travel to Sweden and, by invoke the agreement, stay here for an additional 90 days without a permit. However, the same citizen may not invoke the agreement if his/her stay was in Norway.
Effective visa-exemption agreements entered into before 1993:
USA, Argentina, Australia, Brazil, Brunei, Canada, Chile, Cook Islands, Costa Rica, El Salvador, Guatemala, Honduras, Israel, Japan, Malaysia, Mexico, Nicaragua, New Zealand, Panama, Paraguay, Singapore, South Korea, Uruguay, Venezuela.