RPGs wouldn't seem to work well for this type of thing.. likewise with games like APB where the max group size is 4 (or 6 I think). I think Warframe also limits 4 people to a map I believe and people will get left behind due to the progression requiring you to complete a map before you move on. It really depends on how many people you get in on this.
Like MoonstoneX said, Planetside 2 would be the best game for this type of thing, as everyone can hop in and join the army and play together wise general ease. However, PS2 runs like crap on my computer and I don't really like it anyway hehe.
I'm not sure what you are going for with this, like if you want to get a group going for an MMORPG like, say RIFT, which would be an investment much longer than just friday night, but my assumption would be a quick, easy to run, casual shooter room-based thing maybe with some voice chat. and free of course.
Some suggestions:
F.E.A.R Combat:
http://www.fearcombat.org/
Team Fortress 2 obviously although it is a bit boring
I was going to say Rune but apparently it is not free..
Postal 2 was something I always voted for but it never happened..
http://www.gamershell.com/download_26434.shtml