Since the objective is to make a motor that can push a bike, I think it's fair to include the overall gearing to the wheels in the efficiency measurement.
One measurement would be the watt-hours per km at a specific speed. Anyone with a CycleAnalyst or similar device can make this measurement. This is really what we're after in the end.
Here's an interesting motor design: http://www.evilmadscientist.com/article.php/HomopolarMotor
I made one of these and it always got going so fast the rotor flew off. Now how do you make a brushless version of it?
I once tried taking an old car alternator and shorted the field winding on the rotor and fed the stator with 3 phase from my scooter controller. With the field coil shorted, the thing acts like an induction motor. I don't think I had the drive optimized and it was running open loop, but the thing got spinning really, really fast. So fast that I was worried about it flying apart. Had no torque however.
Here's an interesting coreless axial motor. The magnet is a solid ring that's magnetized with poles in a Hallbach array. There is non-moving back iron behind the coils, so I don't think it is very efficient. You can see the hall sensors in the middle of the upper left coils.
Here's another good motor, the AstroFlight AF3210. This has overlapping windings similar to a Crystalyte hub motor. I wonder how they keep the rotor from flying apart at high rpm?
One of my earlier motor projects was my Zappy motor. After burning it up twice, I replaced the wimpy ceramic magnets with some really strong Neodynium ones that just happen to fit the curvature of the motor housing. This allowed me to rewind the armature with about half the turns of much heavier wire. The result had at least 5x the power of the original motor.