Man, its wierd, but nice, to see Tex, Elledan, and me all in complete agreement in a thread!
Here's a situation in the Trek world:
The ship is facing 3 warships from a hostile race of aliens. The aliens are demanding the ship surrender and leave the area, even though the ship is on a rescue mission.
Here is how various Trek captains would handle it:
Kirk (Star Trek): Kicks all the aliens' butts, makes a speech about freedom, seduces the hot alien princess, completes the mission. Meanwhile Scotty manages to get an extra 1/10 warp out of the engines at the last second, Spock raises an eyebrow, and McCoy says "Dammit Jim, I'm a doctor, not a taxidermist!". Sometime after the battle, a ceiling fan would fall off the ceiling of the bridge, killing a red-shirted ensign instantly.
Picard (TNG): Using brilliant strategy, pulls a great maneuver that forces the other ships to blow each other up. Quotes Shakespeare while doing this. His #2 guy, Riker, then seduces TWO alien princesses. Geordi builds a time machine out of Hubba Bubba bubble gum, and Worf Photon Torpedoes a nearby asteroid... just in case. Data would then punch Wesley in the nose, and turn to the crew and say "You are correct - this is indeed a pleasurable human emotion."
Deep Space 9: None of this would ever happen, as the space station IS STATIONARY. Instead, the crew - bored silly - would re-enact a baseball game from 1943 on the holodeck. Odo would shape-shift into the baseball, but offscreen, as the effect was too expensive.
Voyager: Janeway would try to reason with the aliens - "Can't we all just get along? How about some Tea?", and Enterprise would then get shot repeatedly. Tchakotay would stare in a concerned manner at the monitor. Neelix would run around saying "Nyuk Nyuk Nyuk" while looking for Moe and Curly. The Doctor would smile that "nails on chalkboard" smile.
Enterprise: Captain Bakula would wave a tiny American flag while he flew the ship in loop-de-loops to "Confuse the enemy!". He would do this solely because the Vulcans told him not to. The aliens would then blast the ship, causing Bakula to comment that its the only Warp vessel Earth has, but that perhaps some day we will have more ships, piloted by bald Shakespearian actors. The Vulcan chick would then tell him that the aliens have destroyed the Vurinion Control Cluster, which is located in a vat of melted chocolate in her quarters. Bakula and the Vulcan chick would then have to repeatedly dive into the chocolate naked and wrestle to fix it. The languages expert chick would then announce she has learned to speak "Walleese", and would then talk to the wall for the remainder of the show. No one would notice or care. the doctor would make a pithy comment on humans, while the rest of the crew would lament bitterly that still no one cared enough to remember their names.
Then something totally out of the blue would happen, causing the aliens to get sucked into a black hole. Captain Bakula would then take credit for it, and make friends with the next planet he could find.