They actually do. IIRC, even two US teens having sex with each other in Europe, have technically committed a felony.
http://www.missingkids.com/missingkids/servlet/PageServlet?LanguageCountry=en_US&PageId=1499
Laws Concerning Sex Tourism Involving Children
Federal Laws
18 U.S.C. § 2423 (2008)
§ 2423. TRANSPORTATION OF MINORS
(a) Transportation with intent to engage in criminal sexual activity. A person who knowingly transports an individual who has not attained the age of 18 years in interstate or foreign commerce, or in any commonwealth, territory or possession of the United States, with intent that the individual engage in prostitution, or in any sexual activity for which any person can be charged with a criminal offense, shall be fined under this title and imprisoned not less than 10 years or for life.
(b) Travel with intent to engage in illicit sexual conduct. A person who travels in interstate commerce or travels into the United States, or a United States citizen or an alien admitted for permanent residence in the United States who travels in foreign commerce, for the purpose of engaging in any illicit sexual conduct with another person shall be fined under this title or imprisoned not more than 30 years, or both.
(c) Engaging in illicit sexual conduct in foreign places. Any United States citizen or alien admitted for permanent residence who travels in foreign commerce, and engages in any illicit sexual conduct with another person shall be fined under this title or imprisoned not more than 30 years, or both.
(d) Ancillary offenses. Whoever, for the purpose of commercial advantage or private financial gain, arranges, induces, procures, or facilitates the travel of a person knowing that such a person is traveling in interstate commerce or foreign commerce for the purpose of engaging in illicit sexual conduct shall be fined under this title, imprisoned not more than 30 years, or both.
(e) Attempt and conspiracy. Whoever attempts or conspires to violate subsection (a), (b), (c), or (d) shall be punishable in the same manner as a completed violation of that subsection.
(f) Definition. As used in this section, the term “illicit sexual conduct” means (1) a sexual act (as defined in section 2246 [18 USCS § 2246]) with a person under 18 years of age that would be in violation of chapter 109A [18 USCS §§ 2241 et seq.] if the sexual act occurred in the special maritime and territorial jurisdiction of the United States; or (2) any commercial sex act (as defined in section 1591 [18 USCS § 1591]) with a person under 18 years of age.
(g) Defense. In a prosecution under this section based on illicit sexual conduct as defined in subsection (f)(2), it is a defense, which the defendant must establish by a preponderance of the evidence, that the defendant reasonably believed that the person with whom the defendant engaged in the commercial sex act had attained the age of 18 years.
So a US citizen can be prosecuted for an action that would be totally legal in the country where it occurred if it was performed by a non-US-citizen. There are counties which have age-of-consent being below 18.