Good and difficult questions, all. Sacre is a huge milestone in the history of dance, the kind of work that has achieved notoriety beyond the dance world. It has been labeled as a turning point in the development of western art, tagged as the "first real modern dance", used as a metaphor for the displacement of World War I, and blamed for the eventual dissolution of the Balelt Russe -- not in that order(!)
The original ballet only had a handful of performances, and did not last in permanent repertory. It was, though, the topic of considerable speculation, both academic and artistic. It was, in a way, like Woodstock -- people were proud to claim that they had been in the audience for the event. And like Woodstock, over time it has come to mean almost more as an event than as an actual artwork.
Several choreographers have made work to the score since its 1913 debut, and though some of them have lasted far longer in active repertories, none of them have made the same 'splash' as the original. Most of the dance world thought it was lost beyond retrieval, but historians Millicent Hodson and Kenneth Archer were not convinced it was hopeless. Many of the dancers who had been in the original production had taught what they remembered in various situations, and there were extant renderings of the sets and costumes. Hodson and Archer began to compile all this material, laying out sketches alongside the score. They knew that Marie Rambert, who Diaghilev had hired to assist Nijinsky analyse the score, had made copious notes, but they didn't actually find that document until they were almost finished with their compilation.
Robert Joffrey was an enthusiastic collector of anything having to do with the Ballet Russe -- he'd had Massine set some his early work on the company and encouraged Hodson and Archer to keep working on Sacre -- finally when they were ready to start staging, they worked first with the Joffrey. The version of the work they created, using the Rambert documents to check their work, is not a reconstruction of the original choreography so much as it is a new creation using all those original materials. I cannot say that it is the same ballet, but it is certainly the closest that we can get (time travel being what it is). And in some ways, the hullabaloo this restaging created in the dance world echoed the ruckus the original work inspired.
PBS broadcast a Dance in America program in the 1989, featuring extensive interviews with Hodson and Archer as well as a cleanly filmed version of the company in the ballet. Since then, H and A have staged the work on a few other companies, including the Paris Opera and the Maryinsky -- these have been filmed and broadcast in various places. (see
here for some conversation about film versions) I don't know if anyone has it in their active repertory at this moment, but I imagine it is around and about in the Ballet Russe anniversary programming this year.
If you're interested in some of the history surrounding the work, I highly recommend Shelly Berg's "Le Sacre du Printemps: Seven Productions from Nijinsky to Martha Graham" It's out of print so you might have to interlibrary loan it (try you local college library), but she's an excellent historian and her descriptions of the different works are visceral and evocative.
Like most dance fanatics, you just have to mention Sacre to get my full attention -- it's a fascinating ballet.