I only knew the Internet Archive as a way to see old versions of web pages. I recently discovered they've expanded to offer a large media library, which includes old games like Prince of Persia playable in your browser. It was added to their site in mid-2014, so it may be old news to most here, but I thought it was worth mentioning. With the Internet Archive being such a high-profile website, I can only assume this is somehow okay from a legal standpoint.

https://archive.org/details/msdos_Prince_of_Persia_1990


I'd still like to see the missing games here on GOG, though Ubisoft seems to have no intention to sell the original trilogy anywhere. The upcoming remake of the Sands of Time includes the original 1989 game as unlockable content, but it missed the intended release date by a year. With the previous Forgotten Sands still not on GOG, the odds of it being released here aren't good. Nonetheless, community wishlist entries to show your interest:
Prince of Persia
Prince of Persia 2
Prince of Persia 3D
Prince of Persia: The Forgotten Sands
Prince of Persia: The Sands of Time Remake