Where I am, it is a very odd trip when I have all 10 along.
1. Map - absolutely if I'm going someplace new, but there are places I know more accurately than the map.
2. Compass - likewise
3. Sunglasses and sunscreen - at high latitudes, I'd put DEET before PABA. And a good sunhat before sunglasses.
4. Extra food - it takes a LONG time to starve
5. Extra water - FAR more important than food, but sometimes it is just a way to collect and treat the readily available water.
6. Extra clothes - VERY important here and in many mountainous areas. A warm hat and a trash-compactor bag have big return per ounce.
7. Headlamp / flashlight - Yes! This probably saves my butt more than anything else when the hike goes longer than planned. With LED lights, there no reason not to. But, helpful hint: If you haven't changed batteries in your LED for a long time, you may be surprised just how bright it is again with new battery.
8. First aid kit - Meh. First Aid is in your head more than your fanny pack. Inhaler for an asthmatic kid? Of course. Splints and gauze pads? Not for me. Practice sessions with your pack contents for hemorrhage, broken bones, and exposure? Very good to do beforehand.
9. Fire starter - mini Bic and a square of wax paper.
10. Knife - SAK Classic for me but to each their own.
Priorities for me, in order:
Water - bring it or treat it, likely carry it for some distance.
Light - small LED light
Warmth: Trash bag, hat, fire starting. Likely some other layers.
On more remote trips (i.e. if I don't expect to see anyone else):
Panic button: Cell, PLB, EPIRB, or VHF depending on location and coverage.