For whatever reason, if you wanted to delete an alarm in iOS, you always had to tap Edit, then delete each alarm from there. Finally, in iOS 9, you can just swipe left to delete them.
I doubt this bothered everyone as else as much as it bothered me, but it always annoyed me that you couldn't swipe to delete alarms in iOS. It's not revolutionary, but it's nice to see it here. You can also swipe to delete any world clocks you have in the Clocks app.