Apple - Retrieve old lock screen notifications
Apple messed up, in my opinion, by taking away the "missed" tab on the notification pull down in iOS 8.
The only thing I've found that helps is to navigate to settings > notifications and set "sort by time". After that you can pull down the notification center, and the notifications will still be grouped by app, but at least they are sorted so the most recent group is on top, then you can scroll down reading the top notifications out of each group until you get "caught up"
Personally I used that "missed" tab more than almost another screen on the phone, I can't believe they eliminated it.
Just swipe down from the top of the locked screen. The old notifications will scroll down.
Since this seems to be a popular question, I'll post an updated answer for completeness (and to help anyone searching for the answer on newer devices).
On iOS 11
Let's say you have notifications on the lock screen. You unlocked your device before you had a chance to see them, perhaps because the phone unlocked too quickly, or because you were trying to access an app and didn't have time to check the lock screen notifications.
There is a simple way to see which notifications were on the lock screen again: just pull down the Notification Center from the top of the screen. In it, you'll see the same exact notifications which you had on the lock screen. You will keep seeing these notifications in the Notification Center when you pull it down, until you lock your phone. So essentially you can pull the Notification Center down, deal with lock screen notification 1, pull the Notification Center down again, deal with lock screen notification 2, etc.
What if you want to see your previous lock screen notifications, after you've locked your device? It's simple: just swipe up on either the lock screen or the Notification Center. Then you'll see your past notifications, up to notifications from the past week. It isn't possible to tell which ones are the lock screen notifications that you missed, but you should be able to tell by looking at them – they will be grouped together chronologically.
Starting with iOS 11, the lock screen and Notification Center were updated. Now they have been merged, and have a new name: the Cover Sheet. When you turn your phone screen on, you'll see a locked Covert Sheet. When you're unlocked and you pull down from the top of the screen, you'll be bringing down the Cover Sheet. However, I used the old terms in my answer for clarity.