Xenosaga 1 - 3
Mass effect 1 - 3
DMC 1 - 3
Dark souls 1 - 3
Infamous 1 - 3
Killzone 1 - 3
Jak and daxter 1 - 3

Zelda 1, Zelda 2, and A Link to the Past

In which world that's a trilogy? xD

The Fool's Errand/At the Carnival/3 in Three

The original mainline Zelda trilogy: Legend of Zelda, Adventure of Link, and A Link to the Past.

Well, there's...

-Donkey Kong Country trilogy
-Super Mario Bros. trilogy
-Metroid Prime trilogy

The Witcher. Some people critize the first game but its writing is off the charts.

Other than that Persona 3-5, cheating ofc but I think that's technically the best if you count it. Only one where all three are in my Top 50 games of all-time.

Honorable mentions to MGS, Pokémon and Silent Hill 1-3.

Definitely the original Super Mario Bros trilogy on the NES, as long as we count Mario 2 as "USA" instead of "The Lost Levels". No other trilogy ranks that high for me regarding every entry being of exceptionally high quality. I would probably choose Uncharted and the original God of War trilogy as runners up.

Other good trilogies have at least one weak link. I don't care for Bioshock 2 or Prime 2. DKC 2 and 3 are ok, but nothing special. Resident Evil 3 is kinda meh. And Zelda 2, while I personally hold it in high regards, certainly isn't up to par with the others.

Crash Bandicoot & Pikmin (if you count the first three as a trilogy). There’s also the TFB Skylanders trilogy (SSA, Giants, Trap Team). All go crazy!

If we’re talking about game series that had a perfect 3 game run

Uncharted 2-4
Dragon Age 1-3 (DA2 is a huge guilty pleasure of mine)
Nioh 1-3 (3 is straight up the apex of the genre surpassing 2 in every way)
Bioshock 1-3 (Infinite is another fav of mine)

I would have loved to say Mass Effect, Mafia and Dark Soul but all 3 of their 3rd entries where so weak I just can’t.