Let me first: water bottle. I gonna die if no water. So the water is my essential kit.
Water and/or other drink.
Pump.
A few tools.
Things for repairing punctures.
Tissue paper, in case you have a call or nature, and need to go behind the bushes.
Tools.
Aminos.
Folding bike lock.
Chain Tool and a hydration back pack!!!
Pretty much depends on the length of the expected ride, weather conditions, location (remote/country or urban) and riding level (casual, training, touring, racing).
Always: tire/tube repair kit w/pry levers; spare tube, pump, first aid kit with Dermabond; minor tool kit; helmet; gloves; glasses (higher magnification for spotting holes in tubes); cash/cc/ID in ziplock bag.
Short rides (less than 25 miles or under 2 hours): water optional unless high heat, training/racing, or biking in Death valley. I eat and hydrate properly prior to the ride- no reason for anything regarding food or nutrients of any nature. If remote I will carry a phone.
Long rides (except touring): all of the above, 2 tubes; minimum of two H2O bottles; honey squeeze packs and small amount of food. If racing or organized ride events only 1 H2O bottle (already water stops on the course for you)
Touring (full day plus, no camping): all of the above; various food items; extra H2O, tire (2 if remote); 3 tubes; 4 spokes; major tool kit; lighter; flashlight w/spare batteries; spare phone battery and solar charger; maps!; seasonal clothing/inclement weather gear; beer; another cyclist. Really depends on a lot of variables, but can nearly be the "kitchen sink" if necessary.
Ride Fast, Be Safe!
Howard