1. Launch the phone app and go to the voicemail tab. Make sure that it isn't asking for your PIN. If you're really cautious, you might even call your iPhone and leave yourself a voicemail just to make sure it's working as expected.
Six more easy and necessary steps after the break.
2. Check your passwords for your email accounts and other apps that require password auth, such as Dropbox.
3. Launch the camera. It may need to update its database. You don't want to be stuck waiting for this to happen when you're trying to catch an action shot. After it finishes updating, press the home button to go back to the main screen. That way if the camera crashes you won't have to wait for the database to update. (Trust me on this one.)
4. Check your MobileMe (or ActiveSync) calendars and contacts. Are all of them syncing? Mine did not seem to sync until I launched the calendar and it realized that it needed to fetch them again. (See #2 above 'check your passwords' before this one.)
5. Setup your passcode. iOS 4 lets you choose a "simple passcode" (4 digit PIN) or a more complicated password.
6. If you use MobileMe, go to me.com/find and verify that "Find My iPhone" can find your newly-updated iPhone. If it fails, make sure that location services are enabled as well as push.
7. Check other apps that sync (Simplenote, 1Password, TextExpander, etc) to see if they have current data.
Apple iPhone 6s
Apple iPhone 4