There are several different shoes out there for CrossFit Athletes but which ones should you wear? That depends on what kind of workout you are doing. Here is a quick summary of the differences in the shoes.
Lifters aka Oly Shoes - These shoes have a higher elevated heel and fit tightly onto your foot. You'll want to use these shoes when you are doing squats, cleans, clean and jerks and snatches. Why? The raised heel allows athletes to drop lower, keep their knees out. Great for athletes with ankle mobility problems. However, you should NEVER run or do Double Unders in shoes like these. They are very heavy compared to other shoes and your limited mobility hinders that ability. Not to say you can't do them but you'll regret it quickly.
Nanos, Metcons, No Bull (aka CrossFit shoes) - These are great shoes for any CrossFit athlete. Why? They can handle both running, jump rope movements and also give you enough leverage to do Olympic Lifts like Cleans or Snatch. Would not recommend if you are going a long distance for running nor for long jump rope workouts. These are the most endorsed shoes by major CrossFit atheletes.
Running shoes - These are very flexible shoes. They give athletes the ability to shift weight from heel to toe with no resistance. While they are good for running or jump rope they should not be used for lifts like squats, cleans, press or snatch. Because the athlete can freely shift weight from heel to toe that means they are more likely to have trouble stabilizing on these lifts. If you've ever done cleaned and you put weight onto your toes, the weight of the bar will move forward, making it harder for the athlete to come out of the bottom and chances are you'll miss your lift.
Minimalist/Barefoot - There is some debate about the merits of training barefoot or wearing minimalist shoes (like Vibram Five Fingers). Sports Scientists have done studies on the health benefits of wearing minimalist shoes or going barefoot. Should you decide to try out these shoes please make this change gradual. Your stance and posture will be different from any other shoes your will ever wear. For lifting I would refrain from going minimalist except for deadlifting and the reason is because there is no protection for your feet whatsoever. For running, all I can say is take it easy early on because it is a big adjustment and unless you are only running I can't recommend you use them while doing CrossFit. Also, doing toes-to-bar barefoot hurts!
Don't worry! You don't have to get a pair of each shoe, don't go out and break the bank just yet. A pair of Nanos, Metcons or No Bull shoes are great all around shoes for the stuff we do in CrossFit.
One last thing: remember to clean your shoes out every now and then or else you'll end up with very stinky shoes!