I'm always poking around for odd games, and usually I just find things that have some promise but aren't worth talking about or playing. Today I was pleasantly surprised to discover Last of the Patriots. It's an Amiga-inspired indie game that tries to tell a story without getting all bogged down by combat. It's completely free to download, and I really suggest you give it a try.
Paul Davis, the game's creator, describes it as "a prototype for future games that revolve around plot and character and less on action, with an emphasis on deeper underlying meaning." The gameplay itself is very basic, using just the arrow keys and one button for actions, but its simple gameplay allows it to tell a story in an interesting way.