Are there any animes or mangas based on video games?

Yes, there are many.

Disgaea

Sakura Wars

Clannad

Air

Kanon

Little Busters

11eyes

Animal Crossing

Ef

Galaxy Angel

Final Fantasy

School Days

Shuffle

Kirby

Ys

Street Fighter

Utawarerumono

Chaos;Head

Fate/Stay Night

Da Capo

School Days

Monster Rancher

Pokemon

Power Stone

MapleStory

Ragnarok: The Animation

Sonic X

When They Cry

Kirby: Right Back At Ya!

Megaman NT Warrior

Megaman Starforce

Yes, There are several animes/mangas based on visual novels, action games, card games(trading on interactive), index, and fantasy.

Devil May Cry

Steins;Gate

Chaos;Head

Clannad

H20:Footprints in the Sand

Bible Black

Pokemon

The Legend of Zelda

Digimon

Kirby, Right Back at ya!

Yu-yu-hakosho

Black Heart- Space minus

C---face§(Though the original is not)

Yu-gi-yo

Dragon Ball°series

Final Fantasy

Yes, quite a few, though I can't name all of them. But here are some:

Shining Hearts Shiawase no Pan

Tales of Symphonia

Devil May Cry

Final Fantasy

Fortune Arterial

.Hack

Halo Legends

Little Busters

Ninja Gaiden

Persona 3 and 4

Shining Tears x Wind

Utawarerumono

That's all I can think of, sorry. Hope this helps!

Hmmm... there's a lot of anime out there that comes from SIM RPG-type games. I just list some of them which I think is famous....

Shuffle!

Da Capo

Clannad

Kanon

Air TV

Hey,

I downloaded Phantasia for free here: http://bitly.com/1wTaTXq

it's a perfectly working link, no scam!

The Phantasia action game is a puzzle in which the goal is to rescue dwarves that are imprisoned by the evil wizard.

It's the best game of its category.

I just know:

Fate Stay Night

Final Fantasy

Clannad

Tales of phantasia

Tales of eternia

tales of symphonia

Tales of the abyss

(several of other tales game are in manga form)

Sonic

devil may cry

Fate Stay night - visual novel

tsukihime

clannad

umineko

higurashi

Basically several of them

I use to think Dragonball Z was based off this game called Chrono Trigger, but the only similaritie they had was the same creator

Pokemon, I think all the "tales of " series like Tales of Symphonia, Tales of Grace, Tales of Abyss... But i'm not 100% sure