I haven't done Crossfit but I've read up a lot on it; keeping that in mind, here's an alternate viewpoint:
There's no "right" or "wrong" way to exercise per se, but there are more and less effective ways, and more or less safe ways. Clearly if you participate in a CrossFit program you're going to improve in strength; in a basic sense that's what people are looking for, and Crossfit's certainly not the worst way to go about it.
Here are some things I like about Crossfit: It has a wide variety of exercises, which for some people may help keep them "into" the program, less chance of boredom. If muscle confusion works, then Crossfit definitely has that going for it. The whole "out of the box" feel is very appealing to some people, especially in the Paleo community, which for better or worse loves to do things that go against conventional wisdom (no soap, no shoes, etc.).
Here are some things I don't like: Many popular Crossfit exercises (squats, kettlebells, medicine balls, kipping pull-ups, rope climbs) seem like they have a pretty high potential for injury. Free weights are no more effective than machines (citation needed), but it's a lot easier to drop something/hurt yourself when it's just you and the metal, especially with big weights. And any exercise where you're moving fast and jerking is a recipe for pulling something. Second, there's good fatigue and bad fatigue. If you feel like throwing up, that's bad fatigue. A workout should stimulate your body, but not flood it with cortisol. Also, Crossfit usually gets you on a 3-5 days on, 2-4 days off schedule. If you're working out enough to make a real impact on your body, working out every other day is way too much. Lastly, the whole schtick about "functional strength" is a little silly. My bicep strength is just as "functional" if I got it from a biceps machine as it would be if I got it on a pull-up bar. It's not like machines only make your muscles stronger on a certain angle but if you try to do something real you're actually weak.
It seems a bit like CrossFit is taking a "carpet bomb" approach to exercise - you might hit all the targets, but you probably hit a few churches too. To use a nutrition metaphor, CrossFit is akin to just eating a varied diet and assuming you'll hit all your nutrient needs as a result. Sometimes that's right, but I prefer to track my nutrients and eat a diet that's guaranteed to give me all the nutrients I need. Which is why I do:
HIT. HIT appeals to me because it's a safe, effective workout based on principles of muscle growth. You do an exercise slowly, on machines, 1 set, high weight, and to failure. You do it 1-2 times a week, and you track your progress according to weight and time under load. There's a lot less potential for injury, there's more time for recovery, you're in the gym for 15-30 minutes a week, and the effectiveness has been documented by several studies.
So, is CrossFit "wrong"? No, and for many people it's a good choice. However, I think HIT is a safer and more effective way to build muscle.
For more: http://scottabel.blogspot.com/2012/02/nonsense-that-is-crossfit.html