This is actually a very simple algorithm, basically doing KMeans in the color+(x,y) space. I'm a bit bummed that they named that, since I already tried the same approach a couple of years ago and didn't think it was very useful. Well, apparently it is.
The authors have a nice website with some examples. Unfortunately the linux binary didn't run on my box and building on linux seemed somewhat non-trivial.
So I did what I always do: wrote some Python wrappers. You can find them on github [update] I did an implementation for scikit-image which is now quite mature thanks to some other contributors. I would recommend using that instead if you want SLIC in python.[/update]. The whole thing is pretty small, easy to build and easy to use. Also damn fast (less than a second per image).
There are two variations, one where you can specify the number of superpixels and one where you can specify the number of pixels in a superpixel. Both have an additional parameter, the "compactness", which is a trade-off between the similarity in colorspace and (x,y) space.
Results for varying parameter settings look something like this:
Compare to my (former) favorite, quickshift:
The SLIC implementation converts to Lab, while I didn't do the conversion for quickshift (which I probably should have done).