First invented in 1962 by Martin K. Speckter, it was his belief that advertising copy would be better if one mark was used for surprised rhetorical questions. The name comes from the marks that it's created from: interrogatio is Latin for "a rhetorical question" or "cross-examination"; bang is printers' slang for the exclamation mark
It's hayday was certainly in the late 1960's with some Remington typewriters including it on their keyboards and even until the 1970's Smith-Corona sold replacement key-caps with the interrobang included.
If you're brave enough you can still use it today as it's been included in the Unicode format and is available in several font including Lucida Sans Unicode, Arial Unicode MS, Calibri and is in the Wingdings 2 character set.
So next time you want to shake up your punctuation add an interrobang