[repeating and adding on to other's suggestions]

Map & Compass
Ritter PSK, or at least whistle, signal mirror, tinder, lighter, etc.
AMK "Ultralight .5/.7/.9" or similar FAK, add ACE wrap or coach's tape
Two HeetSheets or poncho
Something to keep you dry in rain and warm in cold, to match the climate/season
Spare dry socks
Something to eat like power bars or other energy snacks, and maybe some tea and/or energy drink mix
Small cookpot or metal cup, and perhaps something like a little alcohol burner.
Something else to carry water in, or at least patches for water bladder [been there, done that]
Water treatment/filtration
Everything in ziplocks to keep things dry.
You have your choice of blades, cordage, etc., in your EDC.

Many, if not most, SAR missions began with a short excursion in a familiar area, where someone got too injured to make it even a short, known distance back out. So, even on easy, quick day hikes, it's well worth letting someone trustworthy know where you're going and when your due back.

For spontaneous or short day hikes, I have a Condor H2O pouch and shoulder strap, with a Nalgene bottle and a metal cup with folded tinfoil lid inside; with a combined mini-FAK and PSK, HeetSheet, iodine tabs and a power bar in the outer pocket.