Refer to this (Army Criminal History Waivers)

Suitability review will be conducted on the following charges (regardless of disposition) prior to any moral waiver processing on all applicants:

Five or more minor nontraffic charges
Two or more misdemeanor charges
Combination of four or more minor nontraffic or misdemeanor charges
One serious criminal misconduct charge
Copy from:
http://usmilitary.about.com/od/armyjoin/a/criminal.htm