COD4 - This game got me into online gaming as a whole, and it's still one of my favorite games. Granted, I don't play it very much anymore however. It was the best of the series, and still is (the mp online now is far too bloated and unbalanced). This was the first game I ever even played online competitively too unless I am going to count being an ass on Socom 3 while at a friends house.
Dragon Warrior Monsters - I played all of these so much; just like pokemon. I chose 2: Tobi's Journey mainly just because I think I played that one the most, I can't quit remember. The way you could breed the monsters you tamed amazed me, and as a kid I logged in over 400 hours. It was insane. I am still waiting for my amazing PS3 version that will have literally every monster ever made for the games in it (and I will be waiting until I die, in since it will never happen).
Resident Evil 4 - The Camecube was my first console, and RE4 was my first M game (or, one that I bought and owned anyway). Not only that, but it is still such a fantastic game. It really raised the bar for me on suspense and such at the time. Dead Space almost topped it, but Dead Space just wasn't as good playing it over and over again. RE4 is still the king for me. Any horror game I play, gets compared to this.
Halo - This, was my first FPS, and it is my favorite series for the 360 (and FPS's in general). It raised the bar so high for me. The giant environments were fantastic, and the co-op got me hooked instantly. Not to mention is was pure fun. I went on and played 2, 3, and Reach. I prefer 2 over all the others, but the first one drew me into the series and set the bar for co-op shooters for me.
Pokemon - Yellow Version was by far my favorite, and this was the first game I ever owned. Back in the day, rollin' on the first Gameboy; this shit was in black and white, and it was AWESOME. I'm not sure if could have set the bar for anything in since it was the first game I ever played, but that means it gets a spot. I always favored Yellow too because Pickachu would follow you around. :3
Golden Sun - This was my first RPG I think? I grew up as a handheld gamer. I had a Gameboy, then a GBC, then a GBA, then... what was it, the SP? The GB that folded and looked like a square. I dunno. After all of those, I finally went on to get a GC, and then a PS3, Wii, and 360. Back to the point though, this game was fantastic. It set the bar for RPGs, and while I'm not sure iof the story can compare to some of my other favorite RPGs I've played (FFXII, Lost Odyssey, Star Ocean, Till the end of time) it was pretty amazing in how you could form different combinations with your dj'inn. Made it dynamic for me, because I wasn't just always looking for better gear.
The Windwaker - This was not the first Zelda game I ever played. I started off with Seasons, and Time (GBC, represent!) and moved on to A Link to the Past, and the Minish Cap. This however, is my favorite one out of all of them. It's just gorgeous. One of my favorite adventure games of all time. It was also my first open world like game I do believe. So it set the bar for that (which has obviously been broken by now). I just thought sailing around and exploring the new islands was awesome; and like I said, the art design. So, so savvy. Oddly enough, I never played the ones from the N64, because I never owned an N64.
Sly Cooper - This, along with Crash Bandicoot are my favorite platforming series of all time, and Sly raised the bar for it back then, and it has yet to be broken. I played this game non stop with my friends back then, and I still adore it (waiting for Sly 4. -.-).
Jak and Dexter - This game, set the standard for almost everything after I played it. The driving, was fun. The shooting was fun. Exploring was fun. The story was great AND funny. I actually wanted to see how it ended. I love this game to death, and want another Jak game. T_T
My list is moreso my "firsts" but those were the games that revolutionized my views on what gaming is, and was. With each one I got a clearer picture of the genres, and what set certain games apart from others, etc, etc.