This video of the first ever public performance of Purple Rain is pretty great.

What makes it special is that it's the actual basis for the studio track. They took that live performance, cut a verse and chorus, added strings and sweetened it up overall. But the core of it is that live track. You can hear noises and voices in the official release that turn out to be crowd noises. You can seem him figuring out that classic closing guitar solo, etc.. Pretty wild.