The Society meets weekly to play these games, using a variety of systems. Personally, I run my games using the Savage Worlds system, a generic universal system which is easily adaptable. When I started, I found that not many people were familiar with that particular system, so I saw a chance to corner the market. I volunteered as a GM, and ran numerous "one-shots", intended to last a single night and using existing characters. These included a horror story, a gritty crime drama, and an Indiana Jones-style adventure.
This term, I'm continuing my role as a GM, but have opted to do a longer-running campaign set during a Zombie Apocalypse. This also involved my players having the choice of making their own characters or using pre-made ones.
As for linking it with writing, I have experimented with that. Not too long ago, I only had two players able to attend, and ran a one-shot using characters from a Work-in-Progress. My favourite thing I took from that involved a player assuming the role of a brawny character picking up enemies and using them as clubs. What TV Tropes refers to as "grievous harm with a body". I don't think I'm going to work that into the story.
I'm planning on doing this on a larger scale for another project.