What are the advantages of the different clipless systems?
I have used SPD and Crank Brothers (I have a set of Mallets on my mountain bike, and Candy SLs on my road bike). Both the Mallet and the Candy are built around the egg beaters.

I have to say I greatly prefer the Crank Brothers. 


Entry/exit is very easy.
They have a decent amount of float, which is great for mountain biking, because it allows you to move around on the pedals if you need to. It's not as great for road biking, but I have the cleats on my road shoes set for the "less float" and the easy entry/exit makes it worthwhile.
No tension screws to adjust, and fewer moving parts to maintain. Just a spring, basically.


This is not to say that the SPD system is bad. Your mileage may vary.