Normally, you can control notifications via System Preferences > Notifications. Unfortunately, iCloud is not listed there. I think Apple may push some people to buy the storage.

To get rid of this notification you can do a few things. You can either stop using iCloud completely by going to System Preferences > iCloud. You can use other, less intrusive services like Dropbox but there might be slightly more work to sync everything you need.

Personally, I limit the usage of iCloud to only essential stuff like contacts, documents so it never gets full. Again, to see available options go to System Preference > iCloud.