In no particular order as I am always using one of the following:
Music
Facebook
Email
Messages
Safari
Camera (ok, that's six. I'm cheating)
Also used very frequently (often several times a day):
Maps
YouTube (especially as a Red subscriber)
Calendar
Notes
Timer (especially via Siri: "set a timer for 5 minutes")
Stocks (and various banking apps for my different financial accounts)
Weather
Flashlight
TV Remote
Slack
Evernote (and companion apps, eg, Scannable)
Various fitness related apps (eg. iSmoothRun)
There are also things like Passbook, some travel related apps (eg. United), Fandango, some games, etc, that I don't use every day, but I use them frequently enough to have them be an important part of my mobile experience.