The nice thing about Borderlands is that you really don't need to follow the story to enjoy it.. but if you want to, it's decent. Cons are that it's a pretty mindless shooter, and as such won't be everyone's cup of tea.
Games on my list I'd like to replay/play/think might work here/co-op/see others play and live vicariously:
Terraria
Civilization V (Depending on how many people would want to jump into an MP game)
Just Cause 2 (I still play this once a month or so, even if it's just for an hour. Go finish a base/town, blow some stuff up, get back to real life. It's currently my "I have 20 minutes to game" game)
Kerbal Space Program (for [MENTION=9789]DieGrootHammer[/MENTION]. If KSP had co-op, I'd immediately jump onto it with you!)
XCOM 2 (It's such a good game, but it gets so disheartening, that I'd really do better with some support!)
Max Payne 3 (I don't think I finished this..)
Homeworld Remastered Collection (A classic that deserves a replay)
Hitman: Absolution (Good replayability, I've seen it for cheap)
Dishonored (Different playstyles work, so good game to chat about and keep a thread active)
Borderlands 2
Shadowrun Returns (Neeeeed to finish this)
XCOM: Enemy Unknown
System Shock 2 (I was shocked at how many people haven't played it yet.)
Commandos 2: Men of Courage (I have no idea how well it performs on modern systems, but it's a goodie)
Metro 2033
The Secret of Monkey Island: Special Edition
Amnesia: The Dark Descent
Don't Starve Together (Did you notice the pun I made with System Shock 2)
Dungeon Siege (No seriously, it was a great pun. Shocked. I crack myself up.)
and [MENTION=2530]Wyvern[/MENTION] and I can play F1 2013.