If you have two-step verification for your Apple ID, you'll also need app specific passwords for any app that uses iCloud starting Oct 1, 2014. You can, and probably should, start now. Fortunately, 1Password will be more than able to handle this extra workload!
Apple will actually generate these app-specific passwords. All you need to do is copy and paste them into whatever password management app you use that can also work in iOS, for example. 1Password has been updated to do that from within iOS 8 and Safari but others can be used to manually copy and paste the passwords.
It is hard for me to understand why Apple puts a 25 password/app limit on this. While I don't have more than a handful of apps that use iCloud, why put any kind of limit on how many a user can have? Are bytes on their servers that limited?! At least you can sign out of
all app's access by simply changing your Apple ID Password.