What martial arts does the US Navy SEALS uses?

Answer 1

They are trained in various disciplines and mix and match as required to overcome their opposition. Very few are dogmatic about style or school because their incentive is not a ranking, a belt or a tournament trophy. They fight only to accomplish their mission, get out and fight again another day.
Navy Seal learn many different forms of hand to hand combat skill, many of them, however are centralized around combat situations, as SEALs are primarily gunnfiters. Hand to hand is only used as a last ditch effort, since since SEALs prefer there advesaries dead to beaten up. For this reason guns>hands.

The main style of Martial Arts is called a Deater System, which inloves many strikes different strikes and rear chokes when employed correctly result in great harm to the individual.

Lastly, it should be noted that one thing that cannot be "taught" by martial arts that all SEALs have, is mental tenacity that ordinary men do not posses. This qaulity can not be "trained" for, it is the overall goal of SEAL training to do nothing more than identifie this quality in individuals. It should be noted that nearly any fighting art induced to a person with the physical and mental tenacity of a SEAL TEAM member will result in successful employment of the given art.