Censorship is a pervasive issue all across the world, but nowhere is it more evident than it is in China. Here, media content falls under extreme scrutiny before it can be released to the public, and video games are no different.
China's Ministry of Culture has, over the years, released public notices denouncing certain games for content-related issues -- games such as Battlefield 4 -- banning them as well as admonishing them.
Games can get banned by the Ministry of culture for a myriad of reasons. Sometimes these reasons are so tenuous or intangible that they don't really make sense. On top of that, ever since the "console ban" in 2000, console games on the whole are technically not allowed in China: since consoles cannot be sold openly in the country, the ministry doesn't inspect these games at all.
On the flipside, there have been games and consoles allowed for sale within the Middle Kingdom. Nintendo was able to release the N64, the Nintendo DS, and the 3DS in China under the iQue brand. The games that are openly sold in China were, of course, approved by the relevant ministries.
Many console games that were ported to the PC were allowed into China as well, even though some PC games are banned; it's common knowledge among Chinese gaming press, for example, that Ubisoft's Assassin's Creed III wasn't allowed to go on sale in China despite not being actually banned.
It's not 100% clear what deems a game unfit for sale in China. The three official criteria are promoting gambling, promoting drugs, and portraying China in a bad light. These pretty much guarantee that Grand Theft Auto will never legally enter China.
The following is a list of 39 games so "bad" that the Chinese government deemed it necessary to openly denounce them. The list is from 2011 and was originally "leaked" by Chinese gaming website 173173.com and gaming forum 3DGame.com.
1) Call of Duty 2
2) CoD 4: Modern Warfare
3) CoD 5: World At War
4) CoD: Modern Warfare 2
5) Shellshock Nam '67
6) Shellshock 2 Blood Trails
7-19) Everything related to Grand Theft Auto
20) Kane and Lynch: Dead Men
21) Kane and Lynch 2: Dog Days
23) Mafia 2
24) Saint's Row
25) Saint's Row 2
26) Total Overdose
27) True Crime: New York
28) Ture Crime: Streets of LA
30) Mercenaries 2
31) 50 Cent: Bulletproof
32) 50 Cent: Blood on The Sand
34) Godfather 2
37 - 39) The whole Siren series.
The following games aren't listed but are publicly known to be banned in China.
Command and Conquer: Generals
Looking at the above list, the biggest "genre" that China seems to dislike are games related to organised crime. It's interesting that the games on the public lists are mostly console games. There are lists of banned PC and mobile games, but they're mostly related to gambling and the like.