Upside Down Flags
The Philippines: The first is the flag of the Philippines. Having one red and one blue stripe, the colors evoke the country's association with the United States, but each stripe holds a designated meaning for those flags in government service.
Normally the blue stripe is flown on the upper half of the flag, but when the country is in a state of war, the red stripe is flow up. This not happened very frequently, but this was seen recently when the flag was displayed incorrectly during this faux paus involving the Obama Administration during a summit in New York.
Thats why all government staffs should have a resident vexillologist
The Rainbow Flag: The flag that you can fly any direction you wish is the Gay Pride flag, designed by Gilbert Baker in the 1970's. Although most people fly this flag with the red stripe on top, Baker designed this flag with the intention people being able to fly it on either orientation because orientation dosn't matter - and thus was created an exceptional vexillological double entendre.
Although the Pride flags with other symbols such as the lamba are not intended to be flown upside down, lest other devices on the flag be shown upside down, the standard seven stripe flag can be flown with the red or purple stripes on top. The Rainbow flag is unique in its use on either orientation, and it speaks volumes to the freedom the Gay Pride movement seeks including the the freedom of orientation.
Just a side note - the Inca/Quechua Flag is quite similar to the Gay Pride flag, and it has a number of variants from six to eight stripes. Just in case you trek through Peru and become rather confused when you see rainbow flags all over the place.