While I've encountered many people who use Fib retracements, I personally don't use them all that much. It's not that I don't find them useful. Rather, I've found other ways to get at the same information - namely something I call "HHPPLs," or Historic Horizontal Price Point Lines. Essentially an HHPPL is a horizontal line that has strong support (or resistance) across a significant amount of time.
Why I prefer HHPPLs
The thing I like about the HHPPL approach is that it forces me to take a broad view of the stock over time. In other words, I can pop in a Fib retracement in the here and now, and get some indicator. While that's not bad, the HHPPL approach looks back in time and asks, "Where has this stock gotten stuck in the past?" My experience has been that the points where it has gotten stuck in the past are good indicators of where it's going to get stuck in the future.
What I like Fib for
The one thing that I do like to use Fib retracements (actually, I believe they're called Fib extensions, or something like that) is in predicting how long an up or down trend will last. Fib extensions don't use the retracement lines. Rather, they extend the Fib sequence into the future, and "guess" where a stock will run out of steam (either heading up or down).
A great example of this is using the Fib extension on the S&P-500 (see image below, as of February 2013). Notice that the Fib retracement/extension at 161.8% showed the overhead resistance around 1475, and the 261.8% extensions is curiously close to the all-time high around 1550. The 423.6% extension is around 1675. So I wonder where this bull market will run out of steam? My bet is somewhere between 1550 and 1675.
Here's another great example of using Fib extensions to help your eye see HHPPLs. Below is a chart of CF as of February 2013. The Fib is drawn from the low December 31st, 2012 to the high on January 30th, 2013. Note that the 161.8 extension nails an HHPPL around $177, and the 261.8 nails another HHPPL around $142.
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