Great question! Here is the info:
Standard for the military drill world (MDW) in America are the M1 Garand, M14, M1903A3 and, to a lesser extent the M1917 (Enfield). There are also some color teams/honor guards that use the Russian-made Krag rifle.
Real, demilitarized rifles are listed here: Pssst, Hey Buddy Wanna Buy an M1903?
Replica rifles are here: Armed Drill Alternatives and The Newest Kid on the Block.
And here is another other alternative: The DrillAmerica Parade Rifle is Here! This is an outstanding light weight rifle (M1903A3) that is the newest addition to the MDW.