For the benefit of those coming here in the future:
I'm using the Xcode 6 beta (4 currently) and targeting iOS 8, and couldn't get my simple notification to work for the life of me. After some research and spelunking on the dev center, it appears that Local Notifications newly require user permission to display notifications (this apparently wasn't the case before iOS 8). Regardless, if you're using the beta dev tools and targeting iOS 8, you'll need to add a little extra code:
[[UIApplication sharedApplication] registerUserNotificationSettings:
Docs for these methods
There are more Types you can include, like Sounds, or Badges on the app icon.
As far as where to place this, You can follow the typical behavior of requesting this permission the first time the user launches the app: in App Delegate's application:didFinishLaunchingWithOptions:, but I chose to call this in addReminder -- the first time the user attempts to use functionality that requires a notification, I request permission to do so.
 "Apps that use local or push notifications must explicitly register the types of alerts that they display to users by using a UIUserNotificationSettings object. This registration process is separate from the process for registering remote notifications, and users must grant permission to deliver notifications through the requested options." From the section about UI Kit enhancements