Do (did) powered airplanes exist where pilots are not in a seated position?
In the first ones the pilot was rarely sitting. Inspired by ships, some early aviators steered their craft by standing upright:


Almost all balloons were and still are flown standing upright. Same goes for all Zeppelins, and they should qualify as powered aircraft.
All Lilienthal glider designs required the pilot to stick the forearm through a tube and grab a horizontal bar, so his weight would rest on the forearm. Steering was done by swinging the legs left or right rsp. back or forward. The legs also doubled as the landing gear, much like in modern hang gliders. Lilienthal experimented with carbon dioxide engines, so some of his gliders can be called powered.
Gustave Whitehead's Number 21 design of 1901 was flown standing upright, but it is disputed that he actually flew it successfully.
The early Wright Flyers were flown in a prone position. Sitting came later.
The Santos-Dumont 14bis of 1906 was flown standing upright. Similarly to the Wrights, Santos-Dumont's later designs like the Demoisielle had a proper seat.




Santos-Dumont training to fly his 14bis (picture source)


The Horten gliders were flown in a prone position so the pilot would present a lower cross section. The Horten IIId was a motor glider version using a 32hp Volkswagen engine, so this should count as powered, too.
Before anti-g suits were perfected, some designs used a prone pilot position to increase the possible g loads. Here is an answer which covers this aspect.
René Leduc's ramjet-powered experimental aircraft used an almost lying position for the pilot to keep the cross section of the centerbody small.


 

Yvan Littolff in the cockpit of the Leduc 021 (picture source)


Most hang gliders use a prone or almost lying position for reducing the drag the pilot causes. The powered ones should also qualify here. Same goes for motor gliders derived from sailplanes, where the pilot position is almost lying, too.