If you're wondering what program did I use to render all the fractals on this site, then Mandelbulber is what you need. Quite remarkably, it's free to use, and offers a great number of possibilities, like hybriding different fractals, ambient occlusion and depth of field. You can even make videos, just by indicating which views should be included. Awesome piece of 3D software.
If you own a tablet or a smartphone, and you want to make some nice interesting 2D fractals, then I highly recommend Fractal Designer. This program is extremely easy to use: you control how the fractal is rendered by graphically indicating which parts of your fractal are self-similar. One more thing I would expect it to have is to include mirroring your images.
Of course, there are many many other fractal renderers available, but these caught my eye lately.