I was wondering if any planes had mounted telescopes with the intent to observe the stars. I understand that the atmosphere itself can warp and hinder incoming light and even completely obscure views on cloudy days. Would it be possible to have a telescope which could account for the speed of the airplane and remove motion blur? Would it even be worth it, seeing as the size of the lens would also be limited? Could we see anything interesting that a terrestrial scope of the same size would miss?

Hobbes has mentioned SOFIA as a great example of this being done. Does anyone have more information on the benefits of a plane mounted telescope over one on the ground for noninfrared observation?

This has been done.

SOFIA is an infrared observatory built into a Boeing 747 SP:


SOFIA takes advantage of the fact that some infrared bands are visible at atltitude, these are attenuated by water in the atmosphere so they're less visible on the ground.
There have been infrared observatories before SOFIA:

The first use of an aircraft for performing infrared observations was in 1965 when Gerard P. Kuiper used the NASA Convair 990 to study Venus. Three years later, Frank Low used the Ames Learjet for observations of Jupiter and nebulae.[20] In 1969, planning began for mounting a 910 mm (36 in) telescope on an airborne platform. The goal was to perform astronomy from the stratosphere, where there was a much lower optical depth from water-vapor-absorbed infrared radiation. This project, named the Kuiper Airborne Observatory, was dedicated on May 21, 1975. The telescope was instrumental in numerous scientific studies, including the discovery of the ring system around the planet Uranus.[21]
The proposal for a larger aircraft-mounted telescope was officially presented in 1984 and called for a Boeing 747 to carry a three-meter telescope. The preliminary system concept was published in 1987 in a Red Book. It was agreed that Germany would contribute 20% of the total cost and provide the telescope.

Other airborne astronomy is more incidental. Around solar eclipses, you'll often see some astronomy flights. Some of these are tourism, others perform science. These are usually passenger aircraft temporarily modified (scopes installed that look through the existing windows). These take advantage of the fact you can lengthen the eclipse by flying along its path, and you can reach eclipses in places otherwise inaccessible.
