Tied with Final Fantasy, it's my favorite series ever. Don't listen to people that say it is kiddie or casual. All the games are quite difficult if you play them on the hardest difficulty, and the hardest boss I've ever fought in any game is in Kingdom Hearts. The story is hit or miss. Some people love it, while some people hate it, but the game play is the series strong point. The game play is simply amazing, especially in the most recent games (BbS/DDD). If you do play the series, don't listen to the people that say that only the console games are important. BbS and DDD have the best game play, and 1, 2, BbS are all necessary if you want to understand the story, but if you care about the story I would strongly recommend you play DDD too.
Kingdom Hearts: 3D>BbS>1>Days>Coded>ReCOM>2 >CoM Final Fantasy: 10>13>7>12>6>4>1>2>10-2
I personally recommend playing all the games in the Kindom Hearts series, with the exception of RE:coded, as it is a side story with no real effect on the series. And I also find the story easy to follow and am quite eager for the series to be finished so I can finally get some closure on all the characters.