Skiing off a cliff, holding the audience in suspense for several seconds, then opening the parachute. In the colors of the Union Jack. Nowadays BASE jumping is seen everywhere, but when this movie came out, no one saw it coming. There are audiences who started applauding at that. Stuntman Rick Sylvester deserves special mention, since he was the guy who actually traveled to Baffin Island and skied off the mountain.
The sequence in general is well done (except for the shots of Moore against a blue screen and the banana yellow ski suit), including Bond skiing backwards and flipping off a ledge.
According to the documentary, Everything or Nothing, this was the moment that Bond changed from a successful media property that happened to be British, to a national British icon.
The opening credits sequence, coming off of that, beautifully underscores one very important fact: even after several stumbles throughout the franchise's history, at the end of the day, Nobody Does It Better than Bond.
Fighting a henchman, who nearly falls off a building to his death but manages to keep his balance by grabbing onto Bond's tie. The henchman reaches out for help, Bond grills him for information. The henchman tells him everything. Then Bond slaps the tie out of his hand and he falls to his death. Bond walks nonchalantly away, saying "What a helpful chap."
The car/motorcycle/helicopter/submarine chase, with the Cool Car to end all Cool Cars. Slightly less serious, but still awesome.
Q: "I want that ready for Akbar's tea party."
The elaborate battle sequence inside the hollowed-out cargo ship, with Stromberg's forces going up against the combined efforts of American, Soviet and British submarine crews. With a lot of nameless sailors making Heroic Sacrifices all over the place.