I just remembered, a game I had mentioned in another thread.
Fragile Dreams would make for a great anime, though I'd have to say perhaps a short series but true to the main story or perhaps even a branching off of the game's ending. The ending is rather vague, and who knows what else the main characters encounter after the ending of the game.
I would say Mass Effect but that's already happening. I like westerns so maybe something like Rockstar's Read Dead Revolver and Red Dead Redemption or Gun would be a good game to turn into an anime. I think Read Dead Revolver would be better since it has some hokey bad guys that might fit in a cartoon setting.
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"You know what you have to admire? A Catholic hit man who blesses himself just before he strangles someone."
Radiata Stories: Though the story may seem rather generic to some, it would make up for it with it's bright and colorful cast of characters.
Mirror's Edge: With it's cutscenes, it may as well have it's own animation.
There are many old-school games that probably could have served to have an anime/ or in some cases would have done better if they had been anime instead of games all together.
Just to name a few that just got shoved under the bus:
Okage:The Shadow King (Playstation 2)
Radiata Stories
Star Ocean 3: Till the End of Time (Based more on the manga)
Valkyrie Profile
Without argument: Kingdom Hearts
Mana Khemia - Not so impressive game, better as an anime perhaps.
For me the ones that I want to be turned into anime would have to be :
Persona 3
Suikoden II
I agree even though both have animes associated with them.
Persona: Trinity Souls takes place 10 years after the end of Persona 3
Suikoden the anime takes place in our future instead of a fantasy world like the games. I would like to see the series done right though as anime.
I also agree with Xenogears as some has mentioned. If they can do the prequal as an anime why cant they do the best part of the whole story.
also agree with Resonance of Fate
a couple others i wouldnt mind seeing are:
Soul Caliber series
FFVIII & IX
Valkyria Chronicles - even though there is an anime probably wont ever see it state side
Bloody Roar
Breath of Fire
The more I play of them, the more I think that the Metal Gear Solid series would make a great anime series.
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"There are two kinds of folks who sit around thinking about how to kill people. Psychopaths, and mystery writers. I'm the kind that pays better."
Somehow I knew you'd say that.
I just remembered, a game I had mentioned in another thread.
Fragile Dreams would make for a great anime, though I'd have to say perhaps a short series but true to the main story or perhaps even a branching off of the game's ending. The ending is rather vague, and who knows what else the main characters encounter after the ending of the game.
Kingdom Hearts! which I know has been said.
Sly Cooper would also be a cool one.
id like Final Fantasies...but last time it wasnt translated, and it was a repeat of a storyline section already done at least twice.

"We are but Dust and Shadows"I second Sly Cooper. Great pick. To go farther I would say that Rachet and Clank, if it has not already been said.
I would say Mass Effect but that's already happening. I like westerns so maybe something like Rockstar's Read Dead Revolver and Red Dead Redemption or Gun would be a good game to turn into an anime. I think Read Dead Revolver would be better since it has some hokey bad guys that might fit in a cartoon setting.
"You know what you have to admire? A Catholic hit man who blesses himself just before he strangles someone."
Radiata Stories: Though the story may seem rather generic to some, it would make up for it with it's bright and colorful cast of characters.
Mirror's Edge: With it's cutscenes, it may as well have it's own animation.
That's all I got for now.
Gears Of War, and props to the OP for mentioning Suikoden, that would be a pretty cool anime.
Shadow Of Colossus would be cool too.
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There are many old-school games that probably could have served to have an anime/ or in some cases would have done better if they had been anime instead of games all together.
Just to name a few that just got shoved under the bus:
Okage:The Shadow King (Playstation 2)
Radiata Stories
Star Ocean 3: Till the End of Time (Based more on the manga)
Valkyrie Profile
Without argument: Kingdom Hearts
Mana Khemia - Not so impressive game, better as an anime perhaps.
Hit me: Final Fantasy VIII or X (Anime Version)
Persona 3
Suikoden II
I agree even though both have animes associated with them.
Persona: Trinity Souls takes place 10 years after the end of Persona 3
Suikoden the anime takes place in our future instead of a fantasy world like the games. I would like to see the series done right though as anime.
I also agree with Xenogears as some has mentioned. If they can do the prequal as an anime why cant they do the best part of the whole story.
also agree with Resonance of Fate
a couple others i wouldnt mind seeing are:
Soul Caliber series
FFVIII & IX
Valkyria Chronicles - even though there is an anime probably wont ever see it state side
Bloody Roar
Breath of Fire