Fan remakes, homages, sequels
Many games become much loved by many fans. Sometimes these fans become disappointed that their favorite games can no longer run properly on current machines, are no longer supported or available, or just never got the sequel that they deserved. Once in awhile one they'll even do something bizarre and unexpected for probably no other reason than to spend more time with their beloved games.
This list will only look at the bigger and more interesting remakes. There are a ton of remakes of old arcade titles and games for early home computers and consoles that aren't terribly complicated or interesting. Including them would make this list a couple of hundred items longer and bury anything that people would care about or want to try out. I'm also trying to avoid unreleased remakes, even if there's a demo available showing off what they have so far. A lot of these get started and never finished.
The nature of these games generally means a swift cease and desist if anyone tried to sell them. As such their authors have no choice but to make them free if they want them released and I've provided download links in the comments.