There aren't really a lot of genres of Bukkake, but rather a different way or additions to them. Here is a simple list that I have came across in the past of this style of sex.
Forced Bukkake:
This is were a willing participant acts or seem unwilling to get a facial shower from several men.Bukkake Summit: Here is where a person receives a bukkake shower but tilts their head back and opens their mouth for the full experience, trying to catch it all. At the end of all the facials the cum is collected and drank by the target of the bukkake shower.
Costume Play Bukkake: Here is where a party or video is made in a theme setting such as a girl wearing a schoolgirl uniform in a schoolroom. She would sit and suck off each guy in a line waiting. The men repeatedly cum in her mouth or face.
Dream Shower Bukkake: This is where the group of men have sex with the target. As one man is having sex the other men watch and cum on the girls face. When the man comes to his climax he cums on her face and the next man in line has sex with her. This one can last a while depending on how many men the target is willing to have sex with.
Snowball or Trade Bukkake: This style of bukkake has two or more targets, which when receive facials swap the cum from mouth to mouth or lick it off of eat others faces.
Cum Play Bukkake: Here is where many men cum on the girls face, after which she plays with the cum. Also the men cum on the girls food and the proceeds to eat the food with the sperm glazing.
The genre of Bukkake that I listed above are just a few. There are many more and there are many that are created everyday. You might want to check back to get new ideas on what can be done with bukkake. I will be listing more styles of bukkake in the future.