On August 29th, 1885, the vehicle that is (mostly) recognised as the first motorcycle was patented. Mostly, because there were some similar vehicle prior to that, and there is argument over whether or not it could be considered to be a true motorcycle, as it had two outrigger wheels - suggesting stability was not all it could be.
The vehicle was the Daimler Reitwagen made by German inventors Gottlieb Daimler (whose name can still be found in car manufacturing) and Wilhelm Maybach, another early pioneer of motor vehicles.
The argument for the Reitwagen being a motorcycle rests on the inclusion of an internal combustion engine, which it did. Only one was every built, though.
Image: Wladyslaw [FAL or CC BY-SA 2.0 de (creativecommons.org/licenses/by-sa/2.0/de/deed.en)], via Wikimedia Commons