Fixed: Microsoft has released an update overnight that takes care of the crashing issue. You can grab it in the Windows Phone store.
Work Around: You can still make calendar entries using Cortana and voice. Thanks to @ctkell for the work around. I also confirmed that you can edit calendar entries with Cortana using voice as well and it does not crash the app.
Reports are streaming in on Twitter this morning that any attempt to either add or edit an entry in the Calendar App on Windows Phone 8.1 will crash the app immediately.
The Calendar App for Windows Phone 8.1 was updated overnight along with the other Bing Apps:
Although there are no visual changes from what I can tell I am sure there was some under the hood updates. However, it is hard to verify that as the app update does not contain any type of change log or notes relating to the update.
The app, along with the other Bing apps for WP8.1, did get a new Terms of Service pop-up that appears the first time you run all the apps after the update.
Whatever the cause of the crashes I hope Microsoft turns around a quick fix because adding and editing items in your calendar is something users do multiple times a day and the last thing Microsoft needs is frustrated users with a buggy app update.