I. AM. Batman!

As far as DC is concerned, Batman Beyond appears to exist in a somewhat amorphous 40-50ish years ahead of whenever the current timeline is. Which good for them, I guess one has to become accustomed to things like that in comics, where characters have aged maybe 10 years or so in the past almost 80 years of publication, but that doesn't do me much good. Best policy for roleplaying someone seems to know when the stuff is supposed to be. Especially if that someone is from the future, as about 90% of the time the question you get first is "What year are you from?"

So I took the dates from the shows and stuff and came up with a few answers.

( bluemoon is a geek about details and reads way too far into things as usual. Do I put too much thought into this? Yes. Yes I do. )

tl;dr: there are (at least) 4 distinct timelines, all of which are arguably canon. Personally I go with the show proper starting in the year 2039, but that's just me. Clearly, there's more than one valid option here.