I use all of them. =p
I find they have different purposes because of their differences.
Photoshop is good for… photoshopping. =p It’s a raster-based program and it’s good at doing the really fancy graphics it’s able to create. Some people use it for designing websites, but I don’t like using it for it (for a reason I’ll list below).
Illustrator is vector based. It’s good for logos and other things that you need to scale. Some people use it for laying out their websites, but not many. I find it ill-suited for that task.
Fireworks is also largely vector-based, though it has some raster (bitmap) tools as well. I love this for doing my website prototypes. The reason is because the shapes are easier to change sizes of, since it’s vector-based. I can just directly change it and see it’s value. I can also change it’s size based on pixels. Photoshop makes it tricky to do this because you have to use the transform tool. Illustrator is better at that, but it’s awkward in other regards.
I recently introduced our designer to it at work. I’m not sure if she has used it much or not… she’s pretty pro with using Photoshop since that’s what she’s used to using.
I personally find Fireworks to be faster. I generally lay out the website in Fireworks, then any special effects that I can’t do in Fireworks, I hop over to Photoshop, create it there (or in Illustrator for things like logos), then pull it into Fireworks with the rest of my layout.
For your own purposes, it’s really personal preference.
However, for a job with a company, it seems like more and more are adding Fireworks to their wish list, so it’s probably good to learn. It’s pretty simple to pick up if you’re familiar with any other modern graphics program.