In the Last Crusade ending, Indy picks the true Grail, heals his dying father, and then lets the cup go when Elsa's fall nearly takes him too. The Grail drops into an abyss and is lost for good, which closes the original trilogy. Spoilers follow.
The choice is the best built set piece in the film, in my opinion. The Grail Knight warns that only one cup is true. Elsa hands Donovan the wrong cup and he ages to death, while Indy picks the right one and uses its water to heal Henry. Earlier traps in the temple test skill and nerve, but this one tests judgment, and that is a smart change of pace after the tank and zeppelin chases. It could be argued that the film saves its biggest stunt for a decision rather than a fall.
Then comes the second test. Elsa tries to take the Grail out of the temple, which collapses, and she falls to her death. Indy almost falls after her, reaching for the cup, and Henry persuades him to let go. Perhaps this is the point of the whole film: the artifact is not the prize, and the son who has spent years chasing relics has to drop one to keep his father. That is a cleaner payoff than the earlier Indy adventures offered, where the artifact decided everything.
Why is it called the last crusade? In my opinion the title points to the Grail quest itself, a final holy mission, and to the fact that this was the last film of the original trilogy in 1989. Harrison Ford returned for Kingdom of the Crystal Skull in 2008. The film's closing shot, filmed in Amarillo, Texas, has the Joneses, Marcus and Sallah riding off together, and that picture still reads as the franchise's farewell.