The LZW patent. It caused us a lot of grief with .gif, but that was primarily because the code was published in various places without it being made clear that it was patented. The method was genuinely innovative (it's the sort of thing that might not have been thought of at all without those people's work - or might have been kept as a trade secret and then lost to society if their business failed - in other words, exactly what patents are meant to cover), and really advanced the state of the art. The RSA patent is similar, and even more dramatic in terms of its effect on what was possible.

(Also note that there are alternative methods for both compression and public-key encryption that do not infringe on the patents)