Shuttlecocks
Yep, that's what they're called: shuttlecocks. They're little things you whack back and forth in badminton. I knew they had a name but couldn't for the life of me remember what it was. Google to the rescue, once again. These are some of the most well-known shuttlecocks, standing 12–15 feet or so high, outside the Nelson-Atkins Museum in Kansas City.