I think I overheard someone say "bajillion" but I don't know if it was one bajillion or plural as in bajillions.
I'd imagine there is an upper limit that can probably be determined by taking a peek in the XML, so why don't I just do that?
Well, normally you just kinda plug in a string until you reach a point that the program doesn't like the length of the slide name, then work out permutations from there, but so far, I've given a slide the ID of "123456789012345678901234567890123456789012345678901234567
8901234567890123456789012345678901234567890123456789012345
6789012345678901234567890123456789012345678901234567890123
4567890123456789012345678901234567890123456789012345678901
2345678901234567890123456789012345678901234567890123456789
0123456789012345678901234567890123456789012345678901234567" and Keynote still opens it. Just dealing with numbers and not including letters, you'd just go 10x10x10x10 etc until you account for each number and you could have more slides than that.
Of course, as others have said, you'll hit a limit as far as memory, hard drive space and other factors are concerned, but, at least from a raw "How many different discrete names can I have for slides" it appears to be a very large set.