I'd think the military is so desperate for more cannon fodder that they'll take anyone.
However, All branches of the military are different when it comes to recruiting standards, but they all have regulations regarding felonies. The military maintains a high "moral" standard for recruits and is the basis for not allowing most felonies. If the felony occurred when you were a juvenile you have a better chance of getting in the military but if the felony occurred as an adult you may have a hard time getting in, if at all. In either case it all comes down to the type of offense and how long ago it was.