I discovered David Martin's Sorting Algorithm Animations yesterday. It's great! I've seen animations like this before, but I like how they're all in one place here and can be run synchronously. The drill down pages give helpful analysis of when each algorithm is a good choice, which the animations then drive home. For example, because it is an adaptive algorithm (i.e., "it takes advantage of existing order in its input"), insertion sort smokes the rest on nearly-ordered data; Python's timsort uses this to good advantage.
These animations have a detractor, it turns out, in Aldo Cortesi. I would point out, though, that Aldo is frustrated by their lack of information about the internals of each algorithm. Point granted. However, I think they are helpful for comparing across algorithms, as above. Aldo's visualizations are a great complement. Timsort, e.g., is a sophisticated algorithm, and Aldo's visualization helps unravel it.