There is an old story about a single engine takeoff in a Learjet.
Now, this is no s**t <g>.
Bill Lear had a fed onboard one of the two prototypes days before the Lear Jet's [sic] introduction at the NBAA show at Reading, PA. The fed was so impressed with the two engine takeoff and landing that he asked Lear if it could takeoff and go around the pattern on one. This was in the days when almost all business aircraft were piston powered and some had a negative climb gradient on one engine (remember the Piper Apache?). Lear knew the plane was light and figured it was worth a try given the
PR potential with the FAA for the pending certification.
Unfortunately, Lear had left the spoilers up from the previous landing and ending up going off the end of the runway in a ball of aluminum. As with the XB-70, the more advanced of the two prototypes was destroyed and Lear had to exhibit an aircraft without much of an interior.
There is an old thread here somewhere about a news report of a single engine airliner takeoff in Africa. Sounds dubious to me but, having flown in Africa, it's too close to call...