I seem to recall that some countries require that my passport does not expire for 6 months from the date when I enter the country. Why?!
My more specific question is: I am a US citizen, my US passport will expire in September 2017. Can I travel to Mexico and Germany this summer (coming back to the US in August)?
Timatic, which is the system used by airlines to determine whether you have the proper documents, and the German Government, provide the actual rule, saying that for Germany, US passports "must be valid for a minimum of 3 months beyond the period of intended stay." This is the actual rule that applies.
I'll note that, according to the US Department of State, you do not need 6 months passport validity for Mexico (just for the duration of your stay), but your passport must be valid "six months beyond planned date of departure from the Schengen area" for Germany. It's unclear to me why the US government acknowledges that the official Schengen rule is three months, yet still recommends six months, which is not the actual rule, but it's not completely imprudent advice given that one can be admitted to the Schengen area for 90 days.
No matter which you believe (and it would be more prudent to follow the more conservative of the two), your passport expiring in September is not going to be sufficient for this trip. I would renew your passport now.
We've had a question in the past on Why do countries require validity of 6 months for passports?
The accepted answer is incorrect about Germany. Your passport must be valid for three months after your planned departure. See http://www.germany.info/Vertretung/usa/en/05__Legal/02__Directory__Services/01__Visa/Schengen_20Visa.html:
on the planned date of departure from Germany, your passport should have at least another three months validity
