Like the title says, any manga that has a game as a central plot. This includes manga like oukoku game, no game no life, liar game, medaka box(kinda?), etc. violence and ecchi aren't a problem as long as it works in the plot.
Though it's also good, manga like last game do not fit this criteria. Thanks!

The Gamer

Are you okay with Survival Game like Battle Royale?
Mahou Shoujo Site
Utsuro no Hako to Zero no Maria (Novel)

Try Game of Death category.

Last edited by dalek at 4:10 am, Jan 21 2014

The Gamer

It's a webcomic manhwa, not a manga. But arguably one of the best written one.

third this
also:
Tonari no Seki-kun kinda
Doubt (TONOGAI Yoshiki)
Natsunokumo
Reset
DICE: The Cube that Changes Everything didn't read it yet but heard it's good

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Saki
Shion no Ou
Real PG
Mondaiji-tachi ga Isekai Kara Kuru Sou Desu yo? (Novel)

A bunch of virtual reality game mangas, like
Sword Art Online
Half Prince
Accel World
(Now that I thik about it, all three of them are adapted from light novels)

And just in case you read only the No Game No Life manga, it was adapted from a light novel too.
No Game No Life (Novel)

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"Thus is our treaty written, thus is agreement made
Thought is the arrow of time, memory never fades
What was asked is given, the price is paid"

Video Games:

+1 The Gamer - Hilarious!! Must read for RPGers.
Log Horizon (originally a light novel) - Never read it myself, but it's about an MMORPG.
Moonlight Sculptor (novel) - MMORPG
Btooom! - real life survival game based on a video game. Has gore. (Though, I dropped it cause the ecchi bits annoyed me. It was like panty shots and stuff. >.>)

Other games:

Hikaru no Go - About Go (the game)
Chihayafuru - Kurada (Japanese card game)
Yu-Gi-Oh - various games
King of Cards - A trading card game

Sorta fits:
Rex Fabula - MC has a gambling-like ability.