I'll do my very best not to spoil anything, because the plot is so damn important (excuse my language...) This is in my opinion one of the best Prof. Layton games. I'd say this is my favorite Prof. Layton story by far.
I've been playing these games for years. While I didn't play them entirely in order, that still did the Layton series justice. The THIRD installment of the franchise, this is almost a tribute to all things Layton, that while every Layton game has its motifs and E. eggs and trademarks, this game manages to take it a level further and celebrate what made Layton so lovable and unique.
The categorization of it being an "anime puzzle game" demeans it - while it does have anime influences and sequences and is a puzzle game - it uses these themes while being so much more. The stories of all the games are wonderful, even at their worst. In my opinion, The Azran Legacy's story felt more forced and stood out a bit from the series, but it was still a great game, which is to say The Unwound Future is all the more wonderful.
It is a tragedy that more people who play games DON'T know of or have played any Layton games - for me, growing up, Layton games were the staple of my participation as a gamer and taught me a very valuable lesson growing up: video games can be great, and can make you FEEL.
And boy, does this game hurt like a bitch because it's so good.
My top three games are Unwound Future, The Diabolical Box, and The Miracle Mask, respectively, but by far, I believe this is the best story (though TDB makes a close second).
In short, just like it's predecessors and sequels (or should I say prequels) the game is a work of art, with what looks to be hand-drawn sets, gorgeous scenery with tons of character. There's a lot to do with the game - Professor Layton knows how to keep you busy. The puzzles are amazing, as per usual. Some of them may be too hard for younger players or people like me who are to dumb, lazy, and impatient to spend the time to finish them all, but luckily, the games are usually more forgiving in that respect. A lot of the puzzles you get to save for later.
You love the characters, but this story has a lot more bittersweet emotion to it - in the Layton cannon, this is the supposed "last episode" of the series (the games coming afterward being prequels). From personal experience, this was emotional.
While I drew some relation and internalization from Diabolical Box, reminding me of relationships with people I knew and being a tender story about love and family (yes, I know, the usual...) TUF again, takes it to a whole other level with it's characters doing all the emotional buildup for us.
I'll try not to hype it up any more, although I easily could - but if you love Layton, you'll LOVE this game. I didn't give it the whole ten because I know people's tastes are different, but as far as alternative gaming material, at least in the late 00's, this is gold. It was even listed on GamesRadar's 25 best DS Games of all Time article, ranking #8. The reason I gave it a 9 out of 10 is out of understanding that maybe some people won't like the game as much as I or other 'near fanatics' would, and out of respect toward expectations - like I said, I don't want them to be too high before anyone plays this...
All in all, whether you've played Layton or not, GO PLAY LAYTON, AND PLAY THIS GAME. THAT IS WHAT A GENTLEMAN WOULD DO.
