I do a few thing to check the motor:
Firstly, remove the post motor filter, and the little diffuser, then turn it on. Can you see sparking? Does it sound ok? Does it whine or get grumbly when winding down when you turn it off?
Once the machine is stripped down, and the motor is in your hand, I spin it by hand and check it spins smoothly, if so then the bearings are ok. Then check the armature (where the carbons sit). It should be a bit dirty, but not horrific. Any pitting, scorch marks or scratches are normally bad news. If you fancy, you can remove the carbon brushes and check the ends are nice and smooth, not chipped etc, but you can usually tell by the armature condition.
Finally, try and pull the belt spindle in and out, no movement is good. As above, I then blow any dust (and palster dust) off, and vac it off with a dusting brush to make it nice and clean. I have stripped motors apart to change the bearings before, which may or may not work, but if you have a pile of scrap motors with good and bad parts it cant hurt to try! I agree with the changing of the carbons though, by the time the damage is done there's not much you can do to save it. If I have a motor in bits to change bearings/armatures around I shine the armature up with wire wool, but don't do this when the motors together as if any wire threads get onto the coil they could short out and cause damage.
After all this, when you have the motor and housing back together and screwed in, connect the switch and mains cable up and fire her up to check operation, and that you havent pulled the motor wires out when putting the motor into the housing, as if you get the whole machine together and looking lovely, and then find it's dead, you have to strip it all back again to plug it back in. Ask me how I know... (I normally tape the connections together now to save having to do this!)