Question: How many solar systems are there in the universe?

Marina De Vos answered on 12 Mar 2013:

Until recently, scientists only knew of one solar system, namely ours. With better equipment and understanding they now have found already 500 systems.
http://spaceplace.nasa.gov/review/dr-marc-space/solar-systems-in-galaxy.html provides a nice history of solar system discovery.

But to answer your question, nobody knows but I guess the sky is the limit.