I remember the 1996 Olympics well, because we were there for part of it.
I watched the gymnastics on TV, and I still think it was the most competitive sporting event I have seen.
Here is a recap from the American perspective:
The Russian and Romanian routines very generally amazing also (as were the Chinese, Ukranian, and the Belarusian routines). But since the U.S. won (and because YouTube is probably still U.S. centric), the U.S. videos were easier to find.