In my time playing DnD, I've seen some pretty dumb things happen, and I've done a few myself. In my opinion, doing the occasional thing that defies common sense, yet still somehow works, is part of what makes DnD great. Even in fully serious campaigns, I think there's always room for a little "Creative problem solving."
So, let's share some of what we've done, or seen done.
In one 3.5 game I played, we needed to sneak into a goblin city to retrieve a cursed gem. We all had no ranks in any stealth skills, so we had to improvise. I made like Solid Snake, and hid under a crate, staying still when a goblin looked our way. Our party Warforged pretended to be a statue in much the same way. Our party druid turned into a baby platypus, and pretended to be a baby platypus. Our party leader did my favorite thing, and simply walked around like he owned the place. When the goblins stopped him, he successfully convinced them that he was just a particularly ugly Hobgoblin. It was pretty good.
I recently played a Bloodrager who was basically a friendly tribal country boy, with a love good, lighthearted roughhousing. He could also crack skulls when necessary, but he liked talking things out instead. Our two-man party came across a very large Ogre on our way to a city, and he smelled the deer we had caught and cooked. He demanded it as tribute, but we had just caught this deer, so we weren't exactly keen to hand it over. I hop down from the wagon, and offer to play a game of "Punch for punch." with the Ogre. If we win, he gets our deer, if I win, we get to go, and I get the fancy sabertooth tiger pelt he has. He punches me, I punch him, I do more damage, and the Ogre asks "Who won?" I had thought the answer would have been known, but since it wasn't, I wasn't about to tell the Ogre that it was me. So I say that we tied, and that we'll give him the deer, and he'll give us the pelt and let us go. The DM and the Ogre laugh, and he says OK. We lost the deer, but I walked away with a cool Tiger pelt.
2nd edition. Using some kind of point system for magic. Only spell left is Cantrip
We are being chased by three ogres UP A tower...
We get to the top, the party is HURTING, fighter man is in the single digits on hit points, cleric is out of healing, etc....
I turn to the ogres and cast Cantrip. Define it as 3 floating balls over my hand (Obvious magic, no real game effect)
"THIS IS THE CANTRIP OF DEATH!!!, You have the count of 3 to turn and run or your skin will boil, and all that shall be left of you is the the dust from your bones"
"1...2..."
One badly failed moral roll later they are running away...