The legal concept you are referring to is known as "extraterritoriality". I'm not sure if it automatically applies to all U.S. laws or just ones that specifically state they apply to US citizens in other countries. Also, it is questionable how often it is (or even can be) enforced. After all how easily can they figure out what you are doing overseas? But it definitely is applicable AND enforced in one area that has been discussed on this board (another typical example is in the field of taxation).
The United States has laws that prohibit sex with minors in other countries and has greatly increased government efforts to combat this problem. On April 10, 2003, the U.S. Congress passed the PROTECT Act (Prosecuting Remedies and Tools Against the Exploitation of Ch*ldren Today Act of 2003)
http://www.house.gov/judiciary/s151conf_002.pdf. This act amended Section 2423 of Title 18, United States Code by striking subsection (b) and replacing it with Section 105. Basically, under this new act, United States citizens or residents who engage in sexual activity abroad with a Ch*ld under 18 can face 30 years in a U.S. prison. U.S. Immigration and Customs Enforcement is now actively investigating American sex tourists abroad and making arrests.
If you don't believe it , here is an ad that the US Immigration and Customs Enforcement Agency in cooperation with the christian organization World Vision has been posting in select countries including Costa Rica:

Now that Bush and his radical right christian allies have won re-election, we can expect the pressure is only going to get worse on the CR government to crack down on sex tourism and to fail to distinguish between innocent whorticulturalists like ourselves and the real scum Ch*ld sex mongers.
Back on the subject of hacking into chica's private e-mail accounts, why bother? First of all, I don't buy the rationalization that because privacy rights are deteriorating worldwide, we should contribute to that and invade someone else's. Also, I agree comparing the ethics of a mutually consensual act (albeit possibly illegal) to a nonconsensual invasion of someone's privacy is a false analogy. Besides, if you have the type of relationship where you can't trust your novia, what type of relationship do you really have. One should just automatically assume if one is going with a DR novia that she is trying to play you at least one way or another. Take the relationship for what its worth - good companionship and great sex - contribute to it only what you are getting out of it and don't delude yourself that it is anything more than that. One does not have "relationships" with such gals, one has affairs.