My experience with Kingdom Hearts:
Lent out a GBA game (I forget which) and borrowed Chain of Memories in exchange. Didn't like it much at all. (Might've borrowed Battle Network 2 at the same time - I recall liking that one a whole lot more.) Lent it back, didn't look back.
Eventually bought a PS2. Picked up Kingdom Hearts with it. Got up to the Tarzan stage, but wasn't really feeling it. Put it down for a few months. Came back later, suddenly was compelled to play the game to completion in less than a month. (Felt kind of proud for that, since this was when I was beginning to notice my backlog issues.)
Immediately moved on to KH2, skipping CoM entirely because I already knew I didn't like it. Was mildly confused as to who Roxas was, but caught on pretty quickly. Played up until the final boss in a short span of time, sat on it for a while, then finally came back and finished off Xemnas. Kind of missed the more platform-y elements that the first KH game had in droves (ignoring that those elements are what make the Tarzan stage a drag - particularly the vine-swinging segments), and the triangle button thing made the game way too easy, but I still liked it.
Tried out Birth by Sleep many years later. Started with Terra. Still in my PSP, still running for like a year straight in Sleep Mode (on charger, natch). Haven't gone back to it in a while... probably should.
So there we are. I like the series, but the first was easily the best of them - more focus on Disney, less focus on whatever the hell is going on in the original universe side of things (seriously, I never fail to get confused by that - and I'm not gonna read that cute summary I've seen out there just yet, because I don't want BbS spoiled for me). I do like how they got so many of the original actors, as well as ones I wouldn't have expected like Christopher Lee, Mark Hamill and Leonard Nimoy.
I kinda wonder what it'd be like if they explored other Squenix properties a bit more closely, though, or perhaps some of the ones Disney's acquired since. Marvel Comics world? Star Wars world? Fullmetal Alchemist world? Chrono Trigger world? I dunno. (Knowing how the plots have gone since the first, though, it'd be confusing as hell either way.)