I keep trying to I can log into my Game Center account keeps saying server is down

Same here. Can't download apps from App Store either. Happening on all devices. System Status page showing all green but it must be a server problem.

Same here, I did not even log out from GC, I found the problem in Hay Day game, as I miss half of my nbrs who are connected through GC. Also am on iPhone 6 Plus and iOS 8.3