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.
I think what surprised me the most about Last of the Patriots is that it doesn't come across as "artsy." It's also not trying to be different for the sake of being different. It just uses old design techniques, and it does them very well. The graphics, sound, and controls all feel exactly like something from the 16-bit era, and yet it manages to not come across as dated.
I guess you could call it an adventure game, but old games are hard to pin into one genre. It involves talking to people, walking around, fighting, and doing quests in a way. Old titles were great because they didn't have to be a "shooter" or an "RPG" -- they could just be games. Every level could be something different and weird. That's why I loved Cinemaware games growing up.
It's free, so check it out for yourself if you enjoy the thought of playing as a burly marine dealing with being drunk and cage fighting.