I can't think of a single accessory that *everyone* needs - we're all different, and have different needs. But these are the ones that I know I don't want to be without:
Zagg HDX screen protector. Not so much for scratches, but to protect *me* from glass shards if I drop the phone and the glass shatters. I like the feel of the HDX, and it doesn't seem to leave as much finger "grease" as bare glass.
Tech 21 Impact Clear Case. Good protection, light and relatively thin, clear, and grippy. I also like the Apple Silicone case, but not as much as this.
For days when I run in the rain (or humid, sweaty, summer days), or I'm at the family summer lake house, I switch to the
Lifeproof Nuud case. I tried the Fre, but I the integrated screen protector made touching the screen hit or miss. The Nuud works fine for me with the Zagg HDX on the display.
The Apple earbuds are ok for casual use, but I almost always use either
Bose SoundSport earbuds or
Plantronics Backbeat Fit BT earbuds. Both are relatively open so that when I am running outside, I still hear things around me. I generally use the BT earbuds with the Nuud case, because the Nuud's earbud connector doesn't always let the inline controls work.
I use both
Amazon Basic and
Anker Powerline+ lightning cables. Both lightning ends fit through the Nuud case opening. I do use the stock cable that came with the phone, but I'm pretty careful with it.
For those days when battery life isn't enough, and I won't be near a place to plug in, I switch to the
Apple Smart Battery Case, or I use the
Travelcard charger. Neither has huge capacity, but both give me more than enough to get through a heavy use day (or a day in poor mobile network signal areas, travel days, etc.)
To me, the best way to carry my phone in the car is the
iOttie One Touch car dock. Their suction cup is like magic - it never releases from my dash.