This is very common term used amongst the homies during any type of one-on-on competition such as Pool and Video Games.
T-Bone: "Damn dawgs...whatcha'll playin"
Drey: "Madden 2003 Fool"
T-Bone: "aaight...I got next"
Commonly used in sports, too, such as at a basketball court. Related is "got last," which means that the person has the game available after whatever group(s) have currently has called next.
Who got next?
We got next and we have our five.
You got next? Who got last?
The act of procuring the rights of playing the game in question, once the current party has departed. Most often used in arcades. Can be accompanied (or atleast used too) by placing your quarter next to the coin slot.
"Sweet, it's a Ms.Pac-Man machine"
"Hey, I got nexts"