us won the war with mexico
Southern Arizona and New Mexico, specifically the Mesilla Valley. This transaction is known as the Gadsden Purchase (1853).
The Zimmerman Telegram.
Only if you return by land; if you take a flight you must have your passport with you.
New Mexico.
Mexico and Canada.
The war with Mexico changed the US border and land holdings significantly. The US was advantaged as it acquired New Mexico to be part of United States.
Take a passport. As a US citizen, you won't have much trouble entering Mexico, but you will have to establish your citizenship to get back.
To fly into Mexico you HAVE to have a passport. As of right now the only way you can get into Mexico without a passport is by land travel, but that will change as of Summer 2009. As of Summer 2009 you will need a passport for any land travel into Mexico and Canada.
Mexico and Canada
Germany. More specifically, the German ambassador in Mexico, Arthur Zimmerman.
Mexico