Kaw says: Generally, API SE, SF, or SG; SH or SJ with JASO MA - SAE 10W40. The viscosity may need to be varied based upon when/where you ride. The chart below is from the 2005 1500 owners' manual.
I have used full synthetic 20w40 for the life of this 2002 1500, ridden in every state except ND and ME. I don't ride in icy weather.
It is important, since we have wet clutches, not to use ANY oil that has friction modifiers in it. It will screw up the operation of the clutch.