There is a fair argument that Fibs are a valid natural pattern which tend to also occur in markets more often than not.
Like most of the posters here, I think they are useful, and should be paid attention to but not at all any kind of support/resistance level to hang your hat on without any further thought.
I personally think that they are worth using in your TA because a) there is fair merit to the theory that we are attracted to seeing (and creating) patterns of specific ratios, whether we are consciously aware of this or not and b) if every schmuck thinks there is a level at price xyz, then there is a level at xyz. Doesn't matter whether it would exist or not without a belief in the Fibonacci level, it can be the definitive self fulfilling prophecy.
For any Bund/T-Note futures daytraders out there, try imposing fib levels on 1 or 5 minute candle charts following NFP figures. You will find that the majority of the time, the move has retracements/extensions that bounce off Fib levels spectacularly well. Obviously it can be a bit tough to trade off technicals in the madness that follows NFP, but if you have CQG or similar software, it need only take you 5 seconds after the first major move is over to set this up.
Surely, this adds some merit to the idea that we have some subconscious attraction to moving markets around at these ratios- I doubt many people care for technicals in the immediate aftermath of a big figure, so the fact that these patterns form without consciously looking for them adds food for thought.....
If you are interested in the true history and theory behind Fibs, I have attached the following document which I'm sure my old boss would be thrilled to know I have offered to you all for free! I have had to cut a great deal of the content out as it is too big a file for ET. If you really want the full copy, you could PM me