THE YOUTH OF THE WORLD: When they ended the 1980 Summer Olympics in Moscow, unsurprisingly no one from Los Angeles was there. President Carter insisted that the IOC not even raise the United States flag in Moscow; instead, the Los Angeles city flag was raised, with IOC chair Lord Killanin urging the "sportsmen of the world to unite in peace before a holocaust descends." While the Moscow closing ceremonies does have its charms, things have improved.
I can't find the handover from Los Angeles to Seoul from 1984, but a UFO flew over the stadium and Lionel Richie and the Non-Threatening Breakdancers of the World partied significantly into the night. But we can observe how Barcelona introduced itself at the end of the Seoul Games (flamenco-rific!), Atlanta at the end of the Barcelona Games (more non-threatening breakdancing, and Izzy!), Sydney at the end of Atlanta, Athens at the end of Sydney, and London at the end of Beijing.
The Sydney 2000 Closing Ceremonies are a favorite of mine because they let Midnight Oil argue in favor of reparations to the country's aboriginal peoples, had songs of vegemite sandwiches (and pilfered flute melody), and Kylie Minogue singing ABBA. From the Idle rumors I've seen, London might just be spicy enough top it, and we'll see what Rio promises for 2016.