One True Pairing 'ship: Mulcahy/Radar. So I'm unconventional.
Canon 'ship: Hawk/Trap, Hawk/BJ. Despite myself.
"If this happens I'll stab my eyes out with a spork" 'ship: Potter/Klinger.
"You are one sick bastard" 'ship: Potter/Sophie.
"I dabble a little" 'ship: Hawk/Burns.
"It's like a car crash" 'ship: Flagg/Anyone.
"Tickles my fancy but not quite sold yet" 'ship: Sidney/Hawk.
"Makes no canon sense but why the hell not" 'ship: Sorry, I can't answer this one. The question makes no sense when applied to M*A*S*H. There's at least something in canon justifying any pairing I like the look of.
"Everyone else loves it but I just don't feel it" 'ship: There really isn't an "everyone but me" pairing in M*A*S*H. Either I see it, or someone else doesn't.
"When all is said and done" 'ship: I can't help it. Radar is cute. I have the same hangups as Hawk. I have the same education as Mulcahy, and the same care for people -- and, just occasionally, the same contempt for them as Winchester. If there was a natural fandom in which I should slash, this is it.