Ideally, my D&D games should be an unholy synthesis of A Confederacy of Dunces and Left 4 Dead. A party of adventurers stupid enough to make raiding death traps for treasure their profession, and smart enough to survive it. For a while, anyway.
So back when I played relatively unmodified third edition, I cobbled together a way for players to gain teamwork-based benefits. Teamwork is a Charisma skill that is in-class for every class in the Player's Handbook.
Each player character contributes points towards a pool of teamwork points that are spent by mutual consent to provide benefits to the entire party. Each player character contributes a number of points equal to their skill ranks in Teamwork plus their Charisma modifier. The party may not have more benefits than there are player characters in it.
These abilities only work if the party is able to communicate effectively with each other and within fifty feet of each other. The player characters may re-spend these points at the start of each session. Each benefit has its point cost listed in parenthesis.
Helping Hand (3)
Part members enjoy a +2 bonus to beneficial skill checks that target other party members, such as Heal and Disguise.
+2 to damage when attacking a target that is flanked by party members.
Ultima Hombre (5)
If all party members save one are unconscious or dead, that character receives a +2 bonus to AC, attack rolls, and spell DC.
Mass Assault (6)
+1 to melee attack and damage rolls when charging on the first round of combat.
+1 to ranged attack rolls and damage if no member of the party made an attack with a melee weapon during the previous round.
Each party member enjoys a +1 morale bonus to their saving throws, so long as at least one other party member is within fifty feet.
Nice Save (9)
If at least one party member is unconscious or dead because of events from during this encounter, cure spells cast between party members heal an additional 50% (round down).
Two To Tango (10)
You may switch spaces with an adjacent party member as a move action that does not draw an attack of opportunity.
Back To Back (11)
If at least one party member is unconscious or dead because of events from during this encounter, all party members gain a +1 morale bonus to AC.
Gitter Done (12)
Party members enjoy a bonus to their initiative rolls equal to their Charisma modifier.
Coordinated Backup (13)
Each party member enjoys a +2 morale bonus to their saving throws, so long as at least one other party member is within fifty feet. This benefit does not stack with Backup.
Take One For The Team (14)
If a party member is reduced to negative hit points by a melee attack, any adjacent party members receive an attack of opportunity against the creature that caused this.
Folies Au Deux (15)
When a party member is knocked unconscious or killed, all party members enjoy a morale bonus to weapon and spell damage equal to their Charisma modifier until the end of their next turn.
Nobody Puts Baby In A Corner (16)
Any party member may take a full round action to allow a single fellow party member within fifty feet to immediately take a five foot step that does not draw attacks of opportunity.
Notes Concerning Retrofitting for Other Editions
For second edition, you may have Teamwork be a general non-weapon proficiency that takes one slot. The player characters receive a number of teamwork points equal to half their Charisma --this method is a little front-loaded, but second edition can handle a slight power bump at the lower levels. Some of the benefits may not work as written for second edition, but I'm sure you can iron out the details better than I can.
These rules will work with fourth edition with very little modification, though I would suggest that is not be used with that version of the game because it is complicated enough.
For first edition, well, this isn't written by some septigenarian so I'm not going to even bother figuring out how the hell it would work for you guys.