X0 is turtles, as recorded in Stephen Hawking’s 1988 A Brief History of Time:
A well-known scientist (some say it was Bertrand Russell) once gave a public lecture on astronomy. He described how the earth orbits around the sun and how the sun, in turn, orbits around the center of a vast collection of stars called our galaxy. At the end of the lecture, a little old lady at the back of the room got up and said: “What you have told us is rubbish. The world is really a flat plate supported on the back of a giant tortoise.” The scientist gave a superior smile before replying, “What is the tortoise standing on?” “You’re very clever, young man, very clever”, said the old lady. “But it’s turtles all the way down!
Whenever this story originally appeared, it does seem to have become popular as a result of Hawking’s retelling:
X must be something that can be pluralized: actors, cans, features, caches, big bangs, cronies, and fraudsters all occur in the variable position. It often seems that if a person suggests that it’s “caches all the way down“, he means that many things in a system may be called something else but ultimately can be modeled as caches. Whether we think of gravity and centrifugal force rather than the balancing of a giant turtle as what holds us on the earth, it doesn’t make much difference in most of our day-to-day actions. I’ve also often heard “it’s X all the way down” as the answer to “but then what? but then what?” type questions–at some point the last thing you understand in a sequence of events is what goes all the way down.
The Snowclones Database 
The origin above (from Hawking) is certainly apocryphal. I expect the reason why Russell’s name so often appears in connection with this snowclone is that he referenced a precursor to it, way back in 1927, in his speech :
I got the impression, when reading Russell, that he was referencing a humorous and familiar old anecdote rather than making up something novel, so the bit about the tortoise is presumably older. On the other hand, in Russell it did not have the famous form at all, so it may not qualify as a snowclone.
Maybe the old lady in the story influenced Terry Pratchett…
Although, in this case, there’s only one turtle, with the addition of four elephants.
I was thinking the same thing Marc, and I’d wager that Pratchett’s pastiche of this (in “Jingo”? Small Gods? Men at Arms? Can’t remember, and the interweb is strangely reticent on the subject and on which book contained the context that I can remember…) was probably far more influential in the phrase’s spread to the internet. Geeks love Pratchett, and geeks love Hawking, but I’d bet dime to a dollar that more of them have read the relevant Discworld novel – 250~300 pages, easily understood and quite amusing – than have ploughed their way through A Brief History Of Time, as famous as it is.
I just heard this little story recently, and I started using the phrase “turtles all the way down” to imply something that is endless, but also completely insane. However, I don’t replace “turtles” with anything, just use the original phrase.
For example:
Co-worker: I sent the email to one guy, but he didn’t know what to do with it, so he sent it to another guy, who also didn’t know, then he sent it to someone else, who ALSO didn’t know. Does this ever end?
Me: nope…it’s turtles all the way down.
Man, I totally thought I was being original when I, er, stole this.
Douglas Hofstadter tells a (better) version of this story in Gödel, Escher, Bach.