Fantastic examples all throughout this thread!
Although I'll say... LOL, a couple of people stretching the definition of "trilogy" and including a random set of 3 games from a given franchise. That's not how it works
Anyway, three trilogies I'm a big fan of are all Street Fighter related trilogies. (Bolded is my favorite within the trilogy).
The CPS-1 trilogy: Street Fighter II
- Street Fighter II: The World Warrior
- Street Fighter II' ("Champion Edition")
-
Street Fighter II' Turbo: Hyper Fighting
The CPS-2 trilogy: Street Fighter Zero/Alpha
- Street Fighter Zero
- Street Fighter Zero 2
- Street Fighter Zero 3
The CPS-3 trilogy: Street Fighter III
- Street Fighter III: New Generation
- Street Fighter III: Second Impact ("Giant Attack")
-
Street Fighter III: Third Strike
Each time one of these games came out, it represented the absolute pinnacle of the 2D fighting game genre. They hold up, to this day. And I still play all of them, to this day.