The Globe Theater that was across from the Thames River in London was designed the way it was for many reasons. It was octagonal shaped and had three stories in order to fit as many people as possible at one time. The eight sides allowed for everyone in the sitting sections to be facing the stage.
Above the roof, there were three huts and a tower. I'm not sure what purpose the huts served, but a flag was flown from the tower on days that the play was showing so that people from across the river would know to come to the theater for the 2:00p.m. show time. Shows had to take place at this time because there was no electricity, so there could not be night shows. The fact that they relied on the sunlight to brighten the theater also explains why the roof did not cover the whole theater. It was very open to allow light and air into the structure.
There were three levels of seating and each one projected slightly beyond the other. This was probably so that they could fit as many people into the theater as possible and so that all seating sections could have a clear view of the stage. Because there was only one show time each day, they wanted to be able to get many people in the audience at one time.
The stage probably projected far out into the crowd for many reasons. First of all, it probably stuck out so that the audience could see distinctly. Also, it probably allowed their voices to be heard better if they were closer to the audience. Lastly, having the stage stick out into the viewers probably made the stage bigger. If it didn't project out as much, it wouldn't be as large and the actors would have less room.