Bearing in mind that I have only played 1, 2, and most of 3:
I expected CoM to matter, obviously, because it mattered to 2.
Initially, I didn't expect anything from 358/2, Dream Drop Distance, or Re:Coded to matter because I understood those to be side stories that fleshed out the world.
I didn't expect Birth By Sleep to matter because that appeared to be a fairly self-contained prequel story with only Xehanort as a connecting link.
And Union Cross was a brower/mobile game that, as I understand it, hadn't even finished it's main story yet, so I didn't expect a connection there, either.
That being said, it was apparent from the trailers pretty early that at least BBS was going to tie to the main story, (Because characters from BBS appeared,) and they did go to the trouble of releasing all those games, so it was obvious pretty far in advance that they would matter. I just got burned out on KH after finally beating 2, so I didn't bother to play all those re-releases.
It's OK, though, I watched a couple lore videos ahead of KH3 and so far I've never really felt like I was lost.