Many Saudis grumble that the royal tribe, with an estimated 7000 princes, has grown too large for the country to sustain the opulent family welfare system begun decades ago by the founder, King Abdel Aziz al-Saud. Prince Abdullah seemed to agree. He put royal family members on notice that they should pay their electricity and phone bills as well as buy their once-gratis tickets on Saudia, the state-run airline. The telephone company reported a huge leap in paid phone bills starting in 2000.
Royal watchers believe that prince Abdullah has retreated somewhat, after an outcry from princes. At 78, the crown prince probably does not have long to institute change after King Fahd dies. Having no full brothers, he needs the support of as many important princes as possible. He may have to tolerate some of their excesses for the time being.
There are over 20,000 Royal family members which include the estimated 7,000 princes.
http://www.nationalguild.com/fridayreports/june_28_1996.html%20
And the following sites say it's 6,000 princes (or "male members", or similar words):
http://www.islamicvoice.com/january.2002/insights.htm
http://www.travel-guide.com/data/sau/sau580.asp
http://www.uni-wuerzburg.de/law/sa__indx.html
So I don't know which is correct, but I'm very willing to believe it could be 6,000 or 7,000 princes and a total of 20,000 family members. That's a lot, and I wonder if they all have diplomatic immunity here!