Well Shelverton, technically the latest game (the one that's coming out soon, I forget the name) takes place in the past, so you get to see how Professor Layton meets his assistant, Luke. In terms of gameplay, they're all similar, but the first one is the toughest in that the gameplay is missing a lot of the features that make the later games better (you'd be surprised how often having the ability to write on the screen can help you with the puzzles).
Although each game has its own encapsulated story, there is cohesion throughout the games. That means if you play 2 (PL & the Diabolical Box), you may spot things from PL & the Curious Village, and the same is true for PL & the Unwound Future.
I own all three and will most likely pick up the next one.
Also, I'm waiting for Professor Layton Vs. Phoenix Wright for 3DS later on.