The saying "third time's a charm" is a ritual for lots of video game franchises. Usually after the third game, they go off into a bunch of spin-off series that can be just as prominent as the original sagas, but ultimately don't recapture that same level of story telling and sense of adventure. From the old Spyro game trilogy, to the resistance games, the modern warfare games, the Jak & Dexter games, the original Devil May Cry trilogy, and now the newer ones, like Borderlands 3's release, there is always a sense of closer that is given when the third game arrives.
My favorite personal trilogy would be the Assassin's Creed Ezio trilogy. It's great to go through a story that links between 3 games, and they all stay true and consistent to the character and the time period/locations that they were set to. You start off as Ezio, literally as a baby that had just been born, and them you play from that point up until when he's an old man that's trying to find the truth of the assassin's order. It's games like that, that have impact on the player where they feel as if they lived through an entirely separate lifetime.
Alternatively, the trilogy could be just a few classic/highly regarded games that are from the same developer. For example, if you were to buy a trilogy from Rockstar Games that included GTA 4, GTA 4: The Ballad of Gay Tony, and GTA 4: The Lost And Damned, or the original three 3D games (III, Vice City, and San Andreas), or even a hybrid trilogy that included Midnight Club 3, Bully, and one of the GTA games. The best trilogies aren't always the ones that follow a consistent story, but that can also provide interesting variation of gameplay and immersion.
Regardless of such, this is just for the sake of having an overall verdict of what may be considered the best trilogy in gaming to date. Obviously everyone has their own favorites and it's opinionated, so we'll just base this on the general reception for a particular trilogy and go from there.
I'd be interested to know which ones, and why? Comment below!