This is an extremely subjective question. I would consider stuff released in the 80's (original Macross, Akira, etc) and prior to be unquestionably old school, but with the kids these days telling me that anything over two years is "old", I'm inclined to say anything over 10 years qualifies.
More importantly, "old school" to me implies that it had an impact on the art - that it was groundbreaking (perhaps this is because I think of the term musically, as in old school hip hop) - so in that regard, any anime that is old enough for the current young generation to not necessarily have seen, and that can be viewed as defining how an older generation views anime and the standards they hold it up to qualifies as old school for me. Hence, Cowboy Bebop may seem a little (not much, really, it's a decade old, now) too recent for me to feel completely comfortable calling "old school", I can see how someone in their late teens or early twenties might view it like that. This is why I think the millennium serves as a useful reference point for old school for now. You can perhaps debate 96-99, but anything 2000 or later seems unquestionably too young for the title, to me.
That being said, five years from now, this arbitrary cutoff date will lose its meaning. *shrug*
I don't think that cleared anything up at all. Erm, sorry.