It's worth the time to play through the first one as its the foundation for all the later games. I recommend not playing Birth By Sleep till you played 1, Chain of Memories and 2 First. I haven't played Dream Drop Distance yet, but it seems like a deviation from the games before.
Playing Order:
(Essential)
Kingdom Hearts 1 (PS2)
Chain of Memories (GBA)
Kingdom Hearts 2 (PS2)
Or play the Final Mix I & 2 (Which contains a PS2 ver. of Chain of Memories)
(Optional but builds on backstory)
358/2 Days (DS)
ReCoded (DS)
Birth By Sleep (PSP)
Dream Drop Distance (3DS) (Not so sure where it goes)