i was the only revenue passenger in F on a united flight once. it was the only time i got the infamous UA priority meal selection. this was a good thing, of course--the cabin was full. strange, but in a different way from the empty cabin.
my favorite low-load experience was a saturday night HSV-ATL flight. it was the last flight of the night on any airline, so the only people on the concourse were the delta gate agent, the space camp rep, and the seven of us flying on the plane. the terminal was incredibly quiet. if i moved in my seat, it echoed. we all laughed when the agent used the PA to call for boarding.
after the terminal experience, being the only passenger behind the exit row on a 737-200 was not all that strange.
during boarding, someone asked a flight attendant if we could all sit in first class. she said she would have let us if it was empty, but there was one passenger up there, and she had to preserve the first class experience for that passenger.