I have been CrossFitting long enough to have run into this problem several times, and now I feel like I've got enough experience under my belt to help others make that call when it's game time!
In my opinion, every CrossFitter should have 3 different types of shoes that cover all the bases. The first of which, is the least expensive(about $40), but yet, probably the most used...the Converse All-Star or Chuck Taylor. These shoes provide a flat, solid sole that is essential for control, balance, and proprioception(sense of knowing where your body is in space). Personally, I use my Chucks for most every WOD I hit, but especially if it involves any combination of heavy lifting and running, box jumps, or any task that requires you to be light on your feet. The downfalls of the Chucks are that they tend to be a little heavier that most of today's "Cross-Trainers", but on the flip-side, you most definitely DO NOT want to be lifting heavy loads in Nike Shox or other "High-Tech" shoes. Honestly, in regards to a "do-all" shoe, simplicity is the key.
The second shoe every CrossFitter should have is a good pair of Olympic Lifting shoes. This may seem overkill for some of you...and it probably is, but when you experience the difference of back squatting, snatching, cleaning, overhead squatting, etc. in Oly. shoes rather than your running shoes(water-beds), you will find the purchase to be a great investment! Oly. shoes provide the firmest and most stable lifting environment. The sole of the shoe is usually made of a wood, plastic, or a dense rubber material that forms a lifted heel. This heel allows the lifter to increase the range of motion in the ankle and knee without sacrificing lumbar tightness, which is usually the first thing to go when in a deep squat. In addition, the sole of the the Oly. shoe is often times wider that a traditional shoe, which allows for a solid lifting foundation that does not compress when under load - allowing the energy you're exerting during a lift to be fully translated into a quality lift!
The last shoe that I recommend everyone has is a light-weight, thin and firm-soled running shoe. This can be a tricky item to find due to the fact that most every running shoe has at least 3 inches of foam or hi-tech shock...thingys forming the sole that compress like a sponge with every step. It is very important that these shoes fit comfortably, as it is likely that you'll be doing most of your longer running WODs in them, as well as some of the WODs that could be done in the Chucks(above). I have recently found a great shoe made by Inov-8 that encompasses all things CrossFit, although I found them to be a little unstable for heavy squatting. Another great option are Five Fingers. I know y'all have seen them - the crazy sock-shoes that have individual slots for your toes. These are an amazing all-around shoe, but require a lot of getting used to. I will caution you to NOT go out for a 10k the first day you have these!!! It takes time to adjust and adapt to these shoes, but when you're ready, they will cover all aspects of CrossFit.
In short, buy shoes that are comfortable, stable, and provide a firm sole. If you can see compression in the sole when walking, they are too soft!
A soft sole = lost energy = failed lifts and slower times!!!