Rap has been featured in many videogames. While no karaoke games have focused solely on rap, the upcoming game Def Jam Rapstar is going to include -only- rap songs from different periods of time. Rap has also been featured in the soundtracks of a lot of games. Games like GTA: San Andreas, Saints Row and other games of the free roam genre have included rap in their soundtracks, and many of these have received critical praise for being well put together. Rap music has also been featured in the Def Jam franchise. While the first two games of that franchise only had rap as a soundtrack, it played a much bigger role in the third entry of the series, Def Jam: Icon. In that game the music played a huge part in fights, because the player was able to activate environmental hazards by closely listening to the rhythm of the current song being played and using it to his/her advantage. Even videogames that are not at all based around Hip-Hop often have rap songs in their soundtracks. These include various boxing and wrestling games, basketball and football games, and more recently a lot of shooters. The games Call Of Duty 4: Modern Warfare and Rogue Warrior for example have both featured rap songs in their ending credits.
Graffiti has been featured in a lot of videogames. Oftentimes walls in open-world games that take place in big cities include walls with graffiti all over them. This can either be a design choice or an actual gameplay element. In the game GTA: San Andreas the player, who takes the role of a gang member, is able to mark his gang's territory by acquiring a spraycan and then finding rival tags and spraying them over. The "Jet Set Radio" games also put a heavy focus on putting up graffiti tags. The challenge in those games is to find the right way to get to a spot where the player can put up his tags, all while being chased by policemen and enemy gangs. Perhaps the game with the heaviest focus on graffiti is Marc Ecko's Getting Up, in which the player can choose from a huge number of graffiti tags, which have to be carefully sprayed onto walls. The game featured complex spraying mechanics in addition to brawling and jump n' run elements.
DJ'ing has not been featured in that many games. The fighting game Def Jam: Icon includes a really basic scratching mechanic, which the player can use to his/her advantage by manipulating the current song being played, or skipping to other parts of the current song being played to set off rhythm-based environmental hazards. Perhaps the game with the biggest emphasis on DJ'ing is DJ Hero, which is the closest thing to actual DJ'ing in videogames. It includes special equipment that simulates actual DJ'ing quite accurately.
Breakdancing has not been featured in many games at all. It is too complex to be done in dancing games that make the player use dancepads. With the recent focus of many developers on motion-controlled videogames, it is very well possible that there may be some breakdancing games coming out.