Would love more team/teamwork challenges. This week I looked for routine PUGs with a bunch of level 1s and then Leroy Jenkinsed with a level 20 templar. And to be honest, I felt a little bad because I knew I was playing selfishly.
I saw some good ideas above, but here are a few more ideas, some crazier than others:
1. Wingman: Earn XXXXX assist XP. (maybe a bit trolly: everyone tries to damage the enemies but avoids actually killing them, hilarity ensues!)
2. No man left behind: play in X games where all 4 people earn immortal medals
3. Bull in a china shop: collect XXXX gold from pots
4. Agoraphobia/hold the fort: finish X last stages where 3 party members do not leave the antechamber.
5. Go down fighting: for one weekend, make the last stage unwinnable (don't stop spawning mobs, make them progressively harder, send out multiple bosses in waves, etc) and make the community goal to make XXXXXXXX final room kills.
6. "Sold his head for good money": Be part of a team that kills XX wyverns.
For each event, give out a brand new, thematic-to-the-event, unique item. Maybe for 1, a ring that heals you when somebody else kills a creature you already damaged. For 5, an amulet that revives you once per game if you are about to bleed out. For 6, if the community reaches it's goal, wyverns will start dropping golden nug-level coin. But ensure that people a) get something cool and

it is not something they could already have. For cool loot put it in the loot table after the event so people not participating can maybe get lucky and find it later.