These are moments that have to be seen to be appreciated. Here are the films and a brief description of the scene.
For Your Eyes Only (1981)
Bond tosses the ATAC device down the sheer cliff-drop where it is destroyed far below. Bond says, ‘You don’t have it and we don’t have it.’ The Russian soldier motions to shoot with his machine gun but General Gogol cries out, ‘Niet!’ and stays the soldier’s hand. The general smiles and makes an approving gesture at Bond with his hands. This is an awesome scene hard to describe. It is greatness personified.
Obtained from wiki above:
Gogol arrives and genially asks for the ATAC; Bond suddenly throws it over the side of the mountain where it shatters hundreds of feet below. Gogol is visibly shocked at first but Bond replies "Detente, Comrade! You don't have it, I don't have it." Gogol suddenly smiles and leaves, obviously humored.
A desperate Bond in his clown suit appeals to the US Base Commander about the hidden Atom bomb. This scene is noteworthy because it showed us Bond’s humanity.
Obtained from Octopussy wiki above:
Bond has trouble getting into the American military base, and gets into the circus disguised as a clown. The American guards let him go after he is identified by Octopussy, and he manages to defuse the bomb just in time.
The Mummy Returns (2001)
Towards the end of the movie, Brendan Fraser’s character and Arnold Vosloo’s character are both hanging on, the pit of hell yawns beneath them. Fraser exhorts Rachel Weisz’s character to get away and save herself but she doesn’t and instead rescues him. The mummy (Vosloo) exhorts Anck-Su-Namun (pronounced Anak-su-namun) to come and help him but she runs away. How Vosloo reacts and what he does next is what makes this such a great scene.
I will add to this if I remember more great cinematic moments.
Where I found info on the Bond films starring Roger Moore:
Idea for a Bond movie:
How about a Bond movie starring Roger Moore as a retired agent who is now a grandfather? His granddaughter is spending the weekend with him. One of his old enemies has tracked him down and invades his country home with a bunch of other thugs. Bond becomes aware of the armed intruders and hides his granddaughter in a safe place (a concealed space prepared years before). He confronts the thugs, perhaps eliminating 2 or 3 of them but he is old now and not as fast as he used to be and is overpowered and disarmed of his Walther PPK. His nemesis appears: it is Drax! It turns out that the one he killed and vented into space (in Moonraker) was a twin brother (or this one seeking revenge is a clone). Bond makes a final witty remark and then the screen goes black for a few moments. Bond was shot and is now dead. His granddaughter survives. Hugh Grant plays the man who married Bond’s daughter, and who finds himself becoming an unwilling participant in the spy game, and who is eventually pitted against Drax-2 who killed his father-in-law, Sir James Bond (knighted due to his years of faithful service).