My calendar won't work on my iPhone 4 since upgrading to iOS8. I am unable to save events
I struggled with this for quite a while. Out of nowhere, I could not add any events or reminders to my calendar, and the (+) in the corner of my calendar was grey. Super frustrating!

Go under settings. Select Mail, Contacts, Calendars.  You must click on individual accounts, and move the slider for calendar to the "on" position. For instance, I have an iCloud account, and multiple gmail accounts listed. I clicked on each account, and turned on all of the calendar sliders.

This fixed the problem, and I am now able to add events, and view birthdays and events.