From the bit I've played, No More Room in Hell can lead to a bit of teamwork. I've found that even if a chunk of your team runs off and gets eaten by zombies, you can still be functional when there's only a couple of you working together.
Project Reality is based around working in a team. Sometimes teamwork on the Insurgent side in the Insurgency game mode is under used, but it doesn't break the game or the mode. It might not be what you're looking for but for teamwork I think it's best I've played :]
*edit: Teamwork is a big main part of Project Reality, so you don't need to worry about being a part of a clan or anything to have it.
For faster paces games though I haven't played team work-y ones lately! A few years back Day of Defeat: Source and Battlefield 2 led to teamwork semi-often.
Natural Selection 2 looks like a recent fast paced game that used lots of teamwork, but I haven't played it.
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