I can hear bats, which I have been told is impossible.
The electrical whine from a crt used to really about me...
I can't hear much at all in a noisy room and sometimes miss whole conversations, which can be bad for one's relationships. I was recently diagnosed with 'auditory processing disorder'. With my 'perfect' sonogram (is that the right word?) in hand, a hearing therapist suggested that I may have lost a tiny bit of my exceptional hearing and that may have triggered my brains confusion with sound.
I once debugged a switchmode power supply this way. I was in my late 20's-early 30's and walked into a room where an engineer in his 50's was testing a power supply. First thing I said, was "what's that annoying noise? Oh, it's coming from your test bench." He blinked at me, but immediately realized that I could hear a high frequency noise he couldn't and that it was related to the problem he was troubleshooting.
IIRC, the problem was that his oscillator was running at a lower than expected frequency: it should have been well outside hearing range but was actually just barely within mine.
Many human ear can hear pure ~28kHz tone under ideal condition [1]. Some can hear higher.
[1] Ashihara, Kaoru (2007-09-01). "Hearing thresholds for pure tones above 16kHz". The Journal of the Acoustical Society of America. 122 (3): EL52–EL57