NASA has flown a ton of unique aircraft as testbeds for research as well as to help find performance opportunities. Here are some unique ones:

AV-8B used for STOL & V/STOL research

YO-3A "Quiet Plane" was a flying acoustic platform used as a microphone to study aircraft noise, especially helicopter noise.

This Bell XV-15 was the second successful experimental tiltrotor aircraft and the first to demonstrate the concept's high-speed performance relative to conventional helicopters. It was later developed into today's V-22 Osprey.

This CH-47B was part of NASA's Variable-Stability Research Rotor Craft project. It was equipped with a fly-by-wire control system in the right seat and three different flight computers.

The F-15 is used as a testbed to this day by mounting a variety of payloads to its hardpoints. In this image, it's testing the X-33's Thermal Protection System

This T-34 is still used today as a chase plane for airborne tests

NASA still flies 2x F-18 Hornets to mount tests to, for instance, they were critical in testing the radar system for the Curiosity and Perseverance rovers. They also operate as high speed chase aircraft.

NASA has had a few C-130's for cargo transport, the latest one is stationed at @NASA_Wallops

There are so many more aircraft, I may add to this tweet chain at another time.