Gandalf, Aragorn, and the knights of Gondor and Rohan vs. a buttload of orcs at the Battle of the Morannon.
You are surrounded. There is no way your tiny group can triumph against the forces of Evil and the Big Bad. Instead of surrendering and trying to bargain your way out, however, you decide to fight it out and go down all guns blazing. This is the Famous Last Stand. This would normally be considered a Very Bad Idea, but in most continua, for some reason, heroes that make peace with their deity of choice and fight for freedom against tyranny, yea, tho' it be with their last breath, often win.
On the alternate hand, if a Famous Last Stand does not succeed, it often rallies the allies of the group to later continue on to victory.
Famous Last Stands should not be confused or even associated with Famous Last Words. The latter are often a surefire way to draw the attention of the Ironic Overpower, and are not generally a good idea if the speaker hopes for things to go at all their way in the near future.
Famous Last Stands in the PPC[]
During the 2008 Mary Sue Invasion, the Sues tried to have a Famous Last Stand at the Tomb of the Unknown PPC Agent. This went... badly for them.
Earlier, at the end of the Black Cats' invasion, Durran Mkellin and his Scout Division had a Last Stand in the cafeteria, which didn't end well for them, either; the only survivor was Jasmine Sims and, unlike other examples, it didn't so much rally his allies as signal the defeat of the Black Cats.
In the course of missions, Mary Sues occasionally try to have Famous Last Stands against the agents. This does not usually benefit them.