I do not know enough to speak about all events throughout the times and places of the vast Roman empire, but typically major events within Rome were free to the Roman people. They were a form of crowd control. Although this would backfire on occassion, especially with horse racing teams, as seen with the Nika revolts in Contstantinople in the sixth century. Citizens were entertained and often even left with prizes (money or food). So at its core the events were meant to keep people happy.

There were no class restrictions as to who could watch, lower classes would often vastly outnumber upper class citizens at these events as they were meant more for them. Much like the present time however, more money meant better seats and a better view. The stands in this sense were divided by class. The free seats for the poor would be at the top while it worked its way down from there as you got closer to the arena floor.

Someone else may be able to go further on this, I'm not an expert on Roman games.

http://www.tribunesandtriumphs.org/colosseum/seating-at-the-colosseum.htm