I included some of my personal favorites, as well as shorts that were acclaimed by others, won awards or simply that I feel more people should watch.
I try to keep it varied, so here you'll find animation and live action, conventional and experimental, documentaries and fiction, comedy and drama, and so on. YMMV, but hopefully there's something for everyone here.
I might add more films to this list if commenters provide films for me to check out, or if I myself start watching films regularly again.
Let me know if you come across links that don't work.