In 2010, Ancel Plaza was home to the graduation ceremony for Barnard College, since the construction of the Diana Center caused Barnard's open lawn (Lehman Lawn) to be too small to host the ceremony.
In 2013, on the night before senior move-out, the Class of 2013 raged on Ancel Plaza. Public Safety was nice enough not to intervene, save to remove some guy who was setting off fireworks.
Students of South Asian descent often use the plaza for cricket games...or did, before heavy picnic tables and benches were strewn across it in Spring 2007.
The Hindu Students Organization holds its annual Holi festival on the plaza, usually in mid to late April. This festival involves lots of people throwing paint (?) at each other, staining the plaza in the process. Like the following video but on a smaller scale: