The Oddworld Series
This is the only game I've ever played that's ever given me an Oddworld feeling. Let me elaborate. The atmosphere in this game is incredibly unique. It was funny, endearing, and yet dreadful, frightening, and uneasy. It's the only game I've ever come across to give me that feeling, which is why I consider it "The Oddworld Effect."
There's something about the art, something about the voice acting, the character design, the writing, the atmosphere, and the ambience that Oddworld owns. It's a series that is near and dear to my heart and it's something that never really got a fair shot. It died in the Xbox/PS2 generation with Oddworld: Stranger's Wrath, despite having a general consensus that the game was an instant classic. I never played Stranger's Wrath, but I have to wonder why something so well received died so silently.
We've seen demand for Oddworld games in HD a lot recently, so maybe, just maybe, they'll get the revival they so rightfully deserve.
The Destroy All Humans! Series
Pandemic Studios was a gaming powerhouse. They built some of the most defining games of my childhood. While I remember them most for Mercenaries and Destroy All Humans!, most people remember them for Star Wars: Battlefront and Battlefront 2. Unfortunately, as of 2009, Pandemic Studios has been shut down by EA. This is my main reason for harboring somewhat negative feelings towards EA, but that's a story from another time.
Destroy All Humans! was the first game I played that put the players in the alien's perspective while being as fun as it could possibly be. Inspired by the science fiction craze of the 1950's feeding off of cinematic classics like Plan 9 and the legends of it's time (Roswell New Mexico,) the game felt like it had a personality of it's own. It was funny, well written, and epic in it's own unique ways and to this day it remains my absolute favorite science fiction game on the PlayStation 2. The comedy, the gameplay, and the physics make this game stand out from most other science fiction games at the time. The sequel, Destroy All Humans! 2 was not only a great sequel, but it improved on many of it's predecessor's elements, while also staying true to the theme of the game's personality.
So, how did it die? Well, Electronic Arts drove Pandemic Studios into bankruptcy, and while Pandemic did later release Mercenaries 2 and The Saboteur on the Xbox 360 and PlayStation 3, EA gave the Destroy All Humans! franchise to a different developer before shutting Pandemic down for good.
Sandblast Games were the heads of the next game in the Destroy All Humans! franchise: Destroy All Humans! Path of the Furon. With the creative team that made the originals what they were gone, we were left with a team trying to impersonate what Pandemic did, and the game turned out, buggy, repetitive, boring, unpolished and uninspired. The game failed tremendously with Pandemic's absence and the franchise was left to die.
I still hope that one day, I'll get that continuation, the Destroy All Humans! 3 that never was. It's unlikely, maybe even impossible, but I can dream.
The Bloody Roar Series
Nobody remembers this game. Nobody. I have yet to find one person to sympathize with on this, but goddamn, is this good. Bloody Roar was a fighting game on the original PlayStation. Unfortunately, this is one of those games who's brilliance I'm not sure I'll be able to convey. You could transform from human characters to human/animal hybrid and it was FUCKING ENTHRALLING. The animations were fluid, the attacks felt powerful, and the fighting styles were unique. The music was adrenaline pumping, the characters had awesome special attacks. I just don't know, this is something you'll have to play to understand where I'm coming from on this. This franchise needs to come back. Killer Instinct on Xbox One? NO! BLOODY ROAR!
If you can get your hands on this game, play it. I recommend Bloody Roar 2, it's the first one I played, and I fell in love with it.
The Legacy of Kain Series
I admit. I was really young when I played this game and the only game I played was The Legacy of Kain: Soul Reaver, but I'll say this. The atmosphere in this game was awesome. It was an adventure game about vampires (that's such a simplified synopsis that I feel bad about it) and it had such a feeling of dread about it. It was awesome. In the same way Oddworld had a unique feeling about it, the Legacy of Kain also had something about it that I can't put my finger on.
You could use weapons in interesting ways, the sound design was top notch, and the characters were awesome. I'd love to see this game come back.
Shadow of the Colossus
A sequel. Seriously, get right on this.