In the past I have used the Look road pedals and the SPD system, however I know that there are many other systems, including some that work purely on magnets.
What are the advantages of the various systems, and when would you recommend them?
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.
This is not to say that the SPD system is bad. Your mileage may vary.
I am a big guy, and have ridden SPD (Mountain bike version, not SPD-R) and Look systems.
I like have the bigger platform to stand and connect with.
Walking in SPD's is usually (depends on the shoe of course) way easier than in Look cleats.
SpeedPlay are pretty good I am told, and some people swear by Crank Brothers Egg Beaters.
I have SPDs on my commuter.
Easy to clip out of, you can walk in the shoes, shoes are cheaper, you can still (just about) use the pedals with ordinary shoes in an emergency.