Is it the number or quality of internships that is more important for Graduate School admission into Computer Science?
The short answer is a lack of internships is not a problem.

The long answer has two cases:


MSCS programs in the United States are profit makers for
universities.  It is much easier to get into an MSCS program at a
top university than the PhD program at the same university. 
Research experience is a plus, but I don't think industry experience
matters.  Grades and recommendations from professors are most
important.
CS PhD programs in the United States almost exclusively admit
students that they are willing to fund, so they are much harder to
get into.  In addition to strong grades and letters of
recommendation, schools want to see that you are capable of working
independently at research.  The best way to do this, as Leon palafox
answered, is to have research experience, including a thesis and/or
publications.  Next best is to have completed projects not required
for any class.  That shows you are capable of doing a project
without its being broken down into lots of steps with intermediate
deadlines.  I'd say Summer of Code-like experience is at least as
valuable as an industry internship.  It shows passion and the
ability to work independently.  Incorporate that into your essay,
and get a letter of recommendation from someone on the project (or
from a professor at your institute if one is nominally supervising
your work for internship or independent study credit).


I am not knowledgeable about admission into programs outside of the United States.