I've gone to roughly twelve sessions. It's expensive, and to me that's the only downside I see. I pay 205 dollars per session, here in Canada. Prices are usually dictated by whichever psychological association sets standards in your country.
As for its effectiveness, I really do think I am in a better position now than a year ago. I don't know how bad I would be if I didn't try to curb the anxiety. As Hypo84 points out, it takes a lot of willpower and a lot of rational thinking, but the therapy was done very incrementally for me - we started with baby steps, we would locate problem areas and come up with small things to try over the next week or two before I had my next appointment. The next appointment would be split - half of the time we would "troubleshoot" the techniques and thoughts from the last two weeks, and the other half we would create new techniques and add to the resources I had at my disposal for helping myself.
Usually these techniques were a combination of mindfulness, breathing exercises, and writing stuff down, getting it out of your head, and working through the fear logically on paper. Lifestyle coaching was also a secondary aim of my therapist - he would help me set realistic goals and help self esteem issues involved with the relapses of anxiety. All in all, I think that it is a positive experience, albeit expensive, and you really need to force yourself to do the work for it. Once you do, it should at least theoretically become more natural. For the span of about eight months I had the hardest time doing the exercises but something just hit me that the only way I can fix this is by doing something to change the way I think. I also came to the realization after a roller coaster of anxiety that one of the keys to breaking a cycle is to just do it, so I started doing things to curb anxiety even if I was feeling extremely bad, although I still have problems doing this when my anxiety levels rise.
Just for perspective, CBT will not cure you of anxiety, it will just make it easier to cope and produce thoughts that are not detrimental to your life and productivity. Since anxiety is a natural human response to danger, it is fruitless to make the goal of CBT to "get rid of it". The first eight months or so of my treatment was like this - doing these techniques to "get rid of it". "Getting rid of" something implies that it is a problem, and "trying" to get rid of something will just increase the thoughts you have about the particular fear or anxiety.
What I finally managed to spit out to my therapist was that I was primarily doing the techniques and exercises to "fix the problem", to which he told me that viewing anxiety as a problem is my first mistake - it is natural, and there is no reason to view anxious thoughts as being more important than regular thoughts. Are they louder? Sure, but as my therapist says, if there is an annoying guy on a bus screaming, what do you do? You can't get off the bus, so instead you move further away from him and limit his annoying presence by taking steps to disregard the validity of what he is saying. Anxiety is this annoying guy.
Just for reference, I would still say that I suffer from severe anxiety, especially under certain circumstances like doctors offices, but CBT has helped me reach a point where anxiety does not completely take over my life or how I do things. I have heart anxiety, and now I am able to climb stairs without fearing a heart attack, and I am not too afraid to exercise.
So, in conclusion, I think that the most important thing to keep in mind if you plan on starting a cognitive behavioral therapy regimen, is to have realistic expectations, and to do the exercises to relax yourself, not to try to get rid of anxiety.