Marko Ramius taking out an enemy sub, with his own totally unarmed.
The President, National Security Advisor Jeff Pelt, Director of Central Intelligence Arthur Moore, Deputy Director Jim Greer, and DDO Robert Ritter successfully tricking the Soviets into buying a totally false cover story, and flushing out a long standing traitor.
Skip Tyler comes up singlehandedly with a plan to convince the Russians that the Red October has sunk.
Admiral Greer: Your full name is Oliver Wendell Tyler? Well, son, if you were named after Harry Houdini instead of a justice of the Supreme Court, I'd... What do you have in mind?
Jack successfuly taking out the GRU agent hiding in the Red October's missile bay.
Worried about the Soviet fleet sailing close to the Eastern Seaboard, the US sends them a message: a flight of four A-10 Warthogs boxing in Kirov, the fleet flagship, with flares standing in for weapons delivery — including anti-tank munitions and the 30mm Avenger cannons they're packing. What makes it even more awesome is that the A-10s were flying at low altitude, almost above sea level, and were being used for the naval strike because they were the first available unit - and antishipping isn't an A-10 mission, but A-10s carry weapons that can kill heavily armored tanks, and what can kill a tank can hurt an armorless ship.
One for Tom Clancy: his novel was so accurate admirals wondered if he was a spy, and he showed them the research done from the library. He's been positively portrayed as an expert ever since.
It's rare for a submarine to get its own crowning moment of awesome, but The Reveal on the Red October is a definite example.
Ramius getting his entire crew to sing the U.S.S.R.'s National Anthem. Even more so when he tells them to keep singing after one of his officers raises concerns about their noise level.
Borodin: And the singing?
[Ramius looks around, contemplating the noise level]
Ramius: Let them sing!
Ramius' navigating blind through underwater canyons as part of an underwater Canyon Chase also qualify. It's exposited that Soviet captains get extremely accurate undersea maps of the canyons with precise times to follow for each leg to allow them to do this safely - which Ramius then proceeds to throw out the window as he navigates round the Neptune Massif by the seat of his pants.
Navigator: Turn plus thirteen, plus fourteen, plus fifteen seconds! Captain, if we're out of position by so much as a boat length...!
Related to the above quote, Ramius is also trying to evade an air-dropped torpedo while still navigating the boat through the canyon; he's deliberately overshot the turn so that when he does finally swing round Neptune Massif, the torpedo's SONAR will be confused by the canyon wall, and track that rather than the boat.
Kamarov: Stop pissing, Yuri. Give me a stopwatch and a map, and I'll fly the Alps in a plane with no windows.
How Jack gets on the Dallas. The guy terrified of flying gets on a helicopter in the middle of a storm to be lowered down on a rope in order to get to the sub, and when it seems the maneuver has failed and they start reeling Jack back in, he waves his arms emphatically to get them to stop. When the pilot ignores him, he, completely straight-faced, releases himself from the rope to fall into the icy cold water below.
Jack: *coughing* How do you do, captain? It's a pleasure to be aboard.
"Give me a ping, Vasily. One ping only, please."
Not to mention the intervention of the USS Dallas, drawing off Tupolev's torpedo and then blowing all its ballast tanks. They may not have been allowed to fire at the Russian sub, but they sure outmaneuvered it. "I hope to Christ this works. Alright, Chief. Put us on the roof."
Jones: WAY TO GO, DALLAS!
Followed by the Dallas practically flying out of the water.