Hmm... I think there are 2 trilogies and a seventh game in the works that looks absolutely nothing like the games before it.
The first one consists of the Curious Village, the Diabolical Box, and the Unwound Future.
The other trilogy is the prequel trilogy, which consists of the Last Spectre, the Miracle Mask, and the Azran Legacy. Azran Legacy has only come out in Japan so far.
There is also a crossover with Ace Attorney, and an iOS game which I mentioned earlier which features Layton's son, Alfendi Layton, and his assistant, which you play as.
There's a movie that takes place between the Last Spectre and the Miracle Mask called "The Eternal Diva".
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You know, I got most of that from Wikipedia.