Unwound Future is the final game in the original trilogy. The next game was a prequel.
You'd definitely enjoy them all more if you played them in order, but if that's not possible for you, then you can still enjoy Unwound Future on its own.
-- Ace Detective in Sir Chris' Police http://i56.tinypic.com/j952zk.gif
I do have a small bit of concern for Professor Layton & the Mask of Miracle just because it's 3D now and not 2D. I never read any japanese reviews for it though, but it's probably still good
any slide puzzle you find throughout the course of the main story usually isn't too bad. It's just the post-game slide puzzles that give you a rough time
I'm maybe halfway through Unwound Future and there has been maybe one or two references I didn't get right away, but that's literally it. The game seems very "standalone" except for a couple small things in 15 hours of gameplay.
It's not that you need to play the games in order to understand the plot, but they are pretty cavalier about spoiling things that happened in earlier games, the assumption being you should already know what happened.
Curious Village, Diabolical Box and Unwound Future sort of form their own little trilogy this way. It's not like the stories are connected, but the later games will spoil some things from the earlier games.
Last Specter, Eternal Diva (the movie), and Mask of Miracle are sort of the same way to each other, but they don't make many references to the other trilogy that much (mostly because they're prequels).
-- Okay, I rolled a 14. What's that mean? Hsu That you're a cheater. This is a 12-sided die. Chan
I think the best argument for playing the games in order is that the series continues to improve as time goes on, in terms of plot, music, puzzles... the works.
If someone started by playing Specter's Flute first and then went back to Curious Village, I can imagine that they might be a bit disappointed.