I was on propranolol for 4 years or so because I was having panic attacks but had an irrational fear of antidepressants, which is what most doctors suggested I try. My logic was A) I'm not depressed, and B) I don't want to mess with my brain chemistry and become normal and boring. I was young.
In a case of cruel irony, I actually became quite depressed during the time I was taking propranolol. (Recent studies suggest this is not coincidence.) It also had no effect whatsoever on my baseline anxiety, which remained uncomfortably high, though it did prevent me from having the actual attacks that I considered my worst symptom.
At one point I stopped taking propranolol for a year. The highlight of this year was losing a prestigious international post-grad fellowship when I had a complete anxious meltdown during my final telephone interview. When it was over, I vomited. After that, I finally gave in and told a doctor to give me the antidepressants (in my case, 75mg venlafaxine).
For me, the effect was immediate, and I can only compare it to a case of cured tinnitus. All of a sudden, this uncomfortable thing that I could feel at all times and that I was always conscious of possibly overwhelming me was gone. Presto. I must say I immediately felt remorseful and a bit stupid for prolonging my suffering for as long as I did by refusing to try antidepressants.
I stayed on venlafaxine until a couple years after my wife and I started dating, at which point I felt like I could taper off, and I did. I'll leave it as an exercise to the reader to look up how much of a pain that can be.
So, my recommendation to fellow anxiety sufferers is to not be afraid to try antidepressants even though you may feel anxiety is the opposite of depression. At least don't settle for a half-cure until you've explored all your options.