How effective is cognitive behavioral therapy for anxiety disorders? How effective have cognitive behavioral therapy type techniques been shown and proven to work for anxiety based on published literature?

Citations please.
Meta-analyses are usually pretty accurate, as they essentially bring together the data from many studies that investigate the same topic of interest together and use statistical methods to effectively get the most conclusive answer possible, throughout all of the studies assessed, just HOW effective is a certain treatment?

For your specific question, there's one in particular that strongly supports CBT for anxiety.  It looks at 71 different studies (that's a ton).  It also investigates it's effectiveness in a variety of different environments and versions of it's therapy.
 It was even published only last month.


  Clin Psychol Rev. 2013 Jul 20;33(8):954-964. doi:
  10.1016/j.cpr.2013.07.003. 
  
  A meta-analysis of nonrandomized effectiveness studies on outpatient cognitive behavioral
  therapy for adult anxiety disorders. Hans E, Hiller W. Source
  Department of Clinical Psychology, Johannes Gutenberg University
  Mainz, Germany. Electronic address: hans@uni-mainz.de. Abstract
  OBJECTIVE: The primary aim of this study was to assess the overall
  effectiveness of individual and group outpatient cognitive behavioral
  therapy (CBT) for adults with a primary anxiety disorder in routine
  clinical practice. METHOD: We conducted a random effects meta-analysis
  of 71 nonrandomized effectiveness studies on outpatient individual and
  group CBT for adult anxiety disorders. Standardized mean gain effect
  sizes pre- to posttreatment, and posttreatment to follow-up are
  reported for disorder-specific symptoms, depression, and general
  anxiety. The mean dropout from CBT is reported. RESULTS: Outpatient
  CBT was effective in reducing disorder-specific symptoms in completer
  (d=0.90-1.91) and intention-to-treat samples (d=0.67-1.45). Moderate
  to large (d=0.54-1.09) and small to large effect sizes (d=0.42-0.97)
  were found for depressive and general anxiety symptoms posttreatment.
  Across all anxiety disorders, the weighted mean dropout rate was
  15.06%. Posttreatment gains for disorder-specific anxiety were maintained 12months after completion of therapy. CONCLUSIONS: ****CBT for
  adult anxiety disorders is very effective and widely accepted in
  routine practice settings.**** However, the methodological and reporting
  quality of nonrandomized effectiveness studies must be improved. ©
  2013.


Across 71 studies, the conclusion used the word "very effective," which is very rare to see in any study in the conclusions section, especially a meta-analysis,  the weighted mean dropout rate across all different types of its application was only 15.06%, AND gains were generally maintained for 12 months (maybe more, I don't have full text) after beginning therapy.

The only caveat they mention is that the methodology and reporting quality must be improved, but I feel that's a general trait that almost all studies need improvement in.
Plus when you investigate SEVENTY-ONE (71) studies, statistical laws start to take over anyway.

Based on this, I'd have to say that there is very, very strong evidence that Cognitive Behavioral Therapy is an effective treatment for anxiety disorders.  

In my opinion, and as an analogy, it's almost just as if not more proven than using aspirin or acetaminophen to relieve a simple headache.  It just works according to the literature, which, if you have that many studies then "routine clinical analysis" really does become reality.  More and more clinical psychologists are switching over to this method or attempting to make some sort of derivative of it.