From Age of Conan to Warhammer Online, a few of the events I've been able to catch are festivals, races, plays, fishing contests, tavern storytelling nights, quests (yes, quests), treasure/scavenger hunts, trivia contests, arena duels, gambling nights, musical concerts, war games, horse races, weddings, dance-offs, terraforming challenges, auctions, jousts, fashion shows, tournaments, funerals, crafter fairs, and more contests than can even be mentioned. These examples aren't restricted to any one genre, either; creatively concocted events run the gamut and include themeparks like Aion, MOBAs like SMITE, and more -- and not just sandboxes.
As you might have noticed, that's quite a bit of content, content that comes at no cost to the the studio! So why is it these events can be so hard to find? With so much free content at their fingertips, it would behoove studios to make it the norm to support and promote these events. And the tools they need to do so are already at their disposal.