Walter and The Dude scattering Donny's ashes at the end of the movie. Immediately after, they get into a loud spat, as The Dude decides that he's finally had enough of Walter's self-important ranting about Vietnam. The high emotions are too much for the outwardly grumpy Walter. Barely holding back tears, he sincerely apologizes, and the two men warmly embrace. Walter's (justly famous) line at the end of that scene is enough to make any grown man choke up.
The whole Mood Whiplash after Donny's death is surprisingly sad, in and of itself. After two hours of crazy intrigue and hijinks, Walter and The Dude can only quietly mourn together, and soberly try to move on with their lives. When they go bowling at the end of the movie (after spending about half of the film's running time in the bowling alley), it's because they need a familiar hobby to take their minds off of their grief—and bowling is the only one they've got. For a stoner comedy about bowling and mistaken identity, the last 15 minutes are a surprisingly realistic portrayal of the grieving process, as many people who've lost loved ones can attest.
The film's use of Townes Van Zandt's cover of "Dead Flowers" in the ending scene, and the following closing credits. (sniffle)
"Take me down, little Susie, take me down, I know you think you're the Queen of the Underground, Send me dead flowers every morning, Send me dead flowers by the mail, Send me dead flowers to my wedding, And I won't forget to put roses on your grave, No, I won't forget to put roses on your grave."