Do graduate students go home for the summer? Is it common or something usual for students to sometimes go home for the summer?
I have seen a wide variety of decisions about the use of the summer break from classes, both in the case of students from the US and those from abroad.  It really runs the gamut.  Examples:


One friend couldn't afford the air fare to visit his home town, during his entire PhD.  This was very stressful for him.
One friend made his good-byes in May and came back in late August married, with his wife accompanying him.  
Some students visit family for part of the summer.
Me: when I needed the money I worked as a secretary in a temp agency over the summer.  Otherwise I enjoyed the break from TA'ing, which allowed me to immerse myself in my exam prep or my project.


It's a very individual decision.  I don't think one should decide about summer plans based on what other people do.