If it is possible for there to be a "classic viral video," then one example is definitely SlackCircus's "What's Going on?" using scenes from the 80s cartoon He-Man and the Masters of the Universe. It is good. Nay, it is great. It was a gem of internet culture in 2005 and remains rather fresh even now. You can watch it below.
Embedded above is a live-action remake of that video by cosplayers at Anime Fest in Dallas. Trevor Lawrence and Thien Vuong led the effort, but they required the assistance of many elaborately-costumed attendees who kindly contributed.