Water of course. Some people prefer hydration packs, most people prefer frame-mounted bottle cages, especially for shorter rides.
Rear-view mirror - essential for safety. There are many different styles and mounting points. Which one you choose is personal preference.
A patch kit and a pump. It can be a mini-pump if you're using it as a backup to a time-saving CO2 system, or a full-sized frame pump if you have room for one and you don't want the waste that goes with CO2 canisters. You never know how many flats you're going to have, even on a short ride if conditions are especially bad - and if you don't have the capability to patch a tube and inflate it after you've exhausted your consumables, you're walking. Even a short ride can be a looooong walk, pushing your bike wearing cycling shoes.
A mini-lock, just to deter crimes of opportunity. Even if you never plan to leave your bike, you may decide to stop for a bathroom break or a snack, and it might be somewhere that you don't feel confident leaving your bike completely vulnerable. A lightweight combination lock obviously isn't suitable for all-day parking, but it's cheap insurance for those bathroom breaks.
A multi-tool. 4, 5 and 6 mm Allen wrenches are enough for adjustments and tweaks, and tightening things that may have come loose, for a short ride. For a long ride in the boonies, a chain tool, spare cables, and the knowledge of how to use them.
Speed comes from what you put behind you. - Judi Ketteler