Depending on the location and purpose of my ride I have a variety of things, but the staples are water, chapstick, knife, a couple horse treats (especially if I’m on a hard to catch horse who might dump me), ID (on me, again in case I get dumped), first aid kit, rain gear, baling twine (I’ve fixed so many bridles, stirrups, hats, belts, saddle bags, etc on the trail with twine!) and an extra lead rope - can substitute for a broken rein, help move a big log out of the way, etc.
If you’re in an unfamiliar area, a map is handy. And sunflower seeds are a great snack as you go. As many others have said, keep that buddy system, whether you have someone with you or just tell someone your itinerary. Have something to take pictures with! I’m a trail guide, so I spend many hours on the trail and can get bored on long quiet rides, so I bring a poem along to memorize or a book to read (when I’m riding a horse I trust and I know the trail well).
Now that I think about it, there’s really not much I DON’T take on day rides…