First trilogy that comes to mind is Prince of Persia (the Sands of Time trilogy).
Each game had its own story arc, while contributing something to the greater arc of the trilogy, which is remarkable in today's popular media where the trend is: First game can stand alone; Second and Third games are one big sequel story in two parts with a HUGE cliffhanger at the end of the Second.
Halo did it. God of War did it. In the world of movies it was done with The Matrix and Pirates of the Carribean.
For me, a good trilogy should work one of three ways:
1) Each part should have a completely stand-alone story and it's the themes and characters that are continually developed throughout the trilogy (example: the first three "Indiana Jones" movies).
2) Each part should have a strong ability to stand on its own story arc while contributing to the bigger narrative. (example: the original "Star Wars" trilogy)
3) They should all flow together in one big story. (example: "Back to the Future" and "The Lord of the Rings")
Yes, I know I used movies for all my examples, but that's a big part of my point: video games
have a big problem of going with the pattern we see in Halo and God of War, and that's NOT a good thing.
Prince of Persia: the Sands of Time is a great video game example of #2. I'd say Metroid Prime is a good example of #1, or possibly #2, depending on how you look at it. I can't think of a video game example of #3. From what I understand, video games are a somewhat riskier business than cinema, so I imagine that building a trilogy like that would be a huge mess.