1) Everyone moves in packs. You never see a graduating senior walking around campus by him or herself on graduation weekend. Instead, those sheathed in the cap-and-gown combo are almost always surrounded by at least one (usually more) adoring family member/friend/groupie. Walking around New Haven with your family, you almost feel like you're in a really uncool gang as you pass by fellow posses heading to their various dinners or events.
2) People clap/cheer at anything said during the ceremonies. Seriously. Anything. The University President could break out in the middle of his speech about sustainability and say "So '30 Rock' really hit its stride this season, huh?" and I am telling you about half of the audience would cheer. He might even get a standing ovation or two, and possibly a few shouts of "Lemon" from the gregarious/restless audience members.
3) You get a new understanding of your friends. There are few games I find more enjoyable than the Watching My Friends Interact With Their Parents Game (I should really trademark that title, huh?). I like seeing if they look like their parents. I like listening to how they talk to their parents. I like figuring out if they have that stand-off-ish/argumentative/weird dynamic or that jovial/friendly/we're-BFFs dynamic. I feel like I am doing a cool, anthropological research project about my friends when I see them with their parents -- and what's more fun than that?!
4) You crave the one or two moments you have to yourself.