I originally just had one request, but now I've got two requests.
The first is probably the worst game I've ever played:
Rallo Gump for MS-DOS.
There's pretty much no information on this game, and for good reason: it's a broken, low-framerate mess.
I got as far as the sixth "world map", and probably would have gotten farther just to see if there was an ending (as I haven't found it documented elsewhere) and probably some latent masochism, but the sixth boss is literally unbeatable for me due to the horrendous collision detection.
The world needs to know about this insult to DOS gaming.
And the second is my favorite indie game:
Iji, an action-platformer from 2008. I enjoyed the atmosphere and weapons, and there's plenty of little secrets to find. One of the notable things about it is that playing pacifistically or just throwing hot plasma in the face of everything that shoots at you does have an effect on the story (but not drastically), and keeping your kill counter low does give you some benefits... but it's a lot more cathartic to play it the way the game expects you to, and the final boss is one of my favorites in gaming as a whole.
Also, the soundtrack is really good.