That's an interesting question to me, especially with these characters that are getting close to a century of stories told about them.
What counts as canon? Theoretically, it's everything that's in continuity that hasn't been retconned, right? With the universe reboots and so on a lot of stuff becomes non-canon, which means with Batman as an example the only stuff that is currently canon in the comics is ... whatever's been published since the last time they fucked with the entire timeline, I don't know when that is.
So, like with Star Wars, there's decades of stuff that's no longer considered canon, right? Anything before Crisis on Infinite Earths, presumably? My understanding is that he managed to keep a lot of his continuity going with the New 52 because whoever was running the character at DC with the Batman family stuff was doing popular work and they didn't want the New 52 to interrupt that, but I don't really know. And since then there's been Flashpoint and Zero Hour and half a dozen universe-altering events, right, so actually very little of the Batman books that have been ever produced actually count as canon right now, right? And that's not counting other Elseworlds and what if stories and things like the comics by the guy who's a Hollow Earther...
And of course, that's not counting TV canon with Gotham, other TV canon with his unseen role in the Arrowverse, other other TV canon (potentially - I don't know how it fits in) with Pennyworth, other other other TV canon (which also had their own comics) with the 60s Batman, and the animated Batmans (whichever ones of those that are linked), and Batman's appearances in other animated shows like Justice League Unlimited... and then there's game canon, and Burton/Schumacher canon, and Nolan canon, and DCU canon, and Harley Quinn/Suicide Squad canon, and Joker canon, and potentially Battinson canon...
It makes a fucking good argument for headcanons, which I generally hate because it's usually how exceptional individuals justify their ships and Everyone Is Trans nonsense.
But there must be an answer, at least for the comics. What, currently, in just the comics published by DC, counts as canon for Batman? It happened recently enough that I'm guessing him almost marrying Catwoman and Alfred dying are part of it. What else? Which Robins? Which groups is he a part of? How is he getting on with others in the DC Universe? Does he use bat-gadgets? What, currently, counts?