Base Wars on the NES- I figured out I could win the game by "disqualifying" the opposing team by repeatedly beaning their batters over and over again until enough of them blew up.
Beach Head II on the C64- I use to enjoy writing words with the machine gun torrent on the stage where one side parachutes troops and tries to make it across the screen to where the gun torrent is holding down its position.
Rampage on the NES- For whatever reason I recall trying to prolong a stage indefinitely by eating the dynamite planting soldiers and thus defending the buildings. Perhaps, and I can't recall the motivation all these years later, I was purposely exasperating the monotony of the game by stretching it by my own volition.
I know that on the big two N64 FPS games (Golden Eye and Perfect Dark), I use to enjoy combing over every square inch of the boards, figuring out what I could shoot/break.
On more than a few games involving flight, I've enjoyed purposely crashing my aircraft.
That's all I can think of at the moment.