I'm working on a special series of meditations, "exercises" really, for anxiety. I'm editing one right now using deep breathing. In it, the first thing I suggest is bringing attention to the anxiety. This is quite the opposite of the usual tendency to want to run away from it. Anxiety builds in a kind of vicious cycle. Anxiety is an expression of fear, and part of what creates it is the fear of the anxiety itself. We resist the anxiety, try to run away from it, and that resistance does indeed cause it to persist. Anxiety, like any other feeling state, comes and goes. Feelings come and go like the weather, but when we get involved in them either through resisting them or ruminating about them, they tend to be prolonged. Let go of the resistance, and the feelings can "pass through".
This is only one small piece of the approach I am using for anxiety, but it is an important one. I'll write more when I've finished my Anxiety Solutions project.
June 2010 Update -- It's almost exactly a year since I wrote this post and we've just finished our anxiety program. What was going to be a series of meditations evolved into a program with meditations, suggested daily exercises and journaling. You can read about it here.