I managed to fix this by showing hidden files in Finder and deleting the Mobile Documents folder.
To do so enter the following in Terminal:
defaults write com.apple.finder AppleShowAllFiles TRUE
After that go to ~/Library and delete the Mobile Documents folder.
Make sure that "Documents & Data" is enabled for the iWork apps and open all the apps. They should now synchronize with iCloud and load all the files without crashing.
It was due to an error with the iCloud syncing process.
I found some "permission denied" errors on the Mobile Backups folder in the ubiquity logs. And a permissions repair did not fix that so I tried deleting the folder and that solved the problem entirely.
This also solves the Keychain Access problem!