In the T.V. series M*A*S*H Radar does something with his hat. I'm wondering what he does with that hat that finishes one of the Leaving episodes.
Are you sure it's his hat? In his final episode before leaving Korea, he left his teddy bear behind, but I don't think he did anything special with his hat.
He was without his hat for most of his final episode, which was actor Gary Burghoff's idea. He wanted to show that the character of Radar was no longer a kid and was grown up, so he went without his hat, which showed off his receding hairline.
Gary Burghoff decided to not wear his hat for the final episode:
No on-screen explanation has been given that I know of.
...and, from the show's final season, well after Radar had left: