So you've got a sweet bike, awesome! The following is a list of all the things you should (or MUST) bring with you!
There is nothing on this list that I haven't had a need for at some point on a ride.
As in, these are required on team rides. And if you don't have them in a race and you have a mechanical, your race is over... you have to carry these items and be able to make repairs yourself.
Helmet!
Water!
Spare tube, of the correct size, etc. Strap it to your frame, carry it in your jersey or pack, or lash it behind your saddle to the rails. Saddle bags are good too, but most of them interfere with the dropper post. Two tubes for long and remote rides. If you've been lucky enough that you've had the same tube strapped on your frame for several years, give it a quick test for leaks, as the rubber can crack along the folds.
Tire levers. A tube doesn't do much good if you can't get your tire off!
Tire inflation. CO2 + chuck, or a tire pump. CO2 is great for a short race where time is critical, but on a longer ride, it's nice to carry a second cartridge or a pump so you're not stranded when you mess it up.
A master link, of the correct type for your chain. It isn't a sure thing that your coach or teammates will have master links that work for your bike. Chains break all the time, this is second in importance only to the ability to fix a flat. I carry two, and have been on rides where I've used both. I like KMC. They can be reused a couple times, but don't overdo it, lest you find your chain coming apart by itself mid-race (not that's ever happened to me, as far as you know).
A multitool with a chain breaker. A master link doesn't help much if you can't remove the old broken link. And there are a whole bunch of other things you might need to tighten, etc.
Not absolutely required, but highly recommended.
A bell, especially for practices at trails with blind corners. Lead rider on downhills should have one, and given how things spread out, best if everyone does. I like the Timber Bell because you can turn it on and off, and you don't need to remember to use it at every turn.
Eye protection.
Gloves.
Essential medications, if you use them. Inhalers, epinephrine, etc.
A tire boot. A dollar bill might work for repairing a sidewall tear, but I find that an old Clif bar wrapper or gel packet is much stronger. I used a dollar bill 10 miles from a trailhead, and the tube pushed through a split in the bill, making it the most careful retreat I've ever had to make, over a too-long distance.
A spare derailleur hanger. This part is designed to break before your frame, meaning that it's not hard to get stranded if you shear it off in a rock garden. These are specific to your bike, so nobody can help you if you don't bring one.
A small bottle of lube. Squirt makes a nice tiny one. When chains get wet and dirty, they break. If you hear a lot of noise from your drivetrain, try to get some of the muck off with your water bottle, and give it a quick lube. Much faster than a trailside chain repair. If you participate in cultish behavior like waxing your chains, bad conditions can trash them very quickly. (Squirt is literally just water and wax, so you won't need to re-clean it if you have to do a trailside re-lube).
Water sufficient to get you through the ride. In particular, bring more if it's warm or hot out.
Rain shell if cooler or possibility of rain.
Head band, bandana, etc. - something to keep sweat or rain out of your eyes if you have problems with this.
Sunscreen, preapplied to exposed skin.
Phone, charged, and with important numbers saved
Mostly if you're heading out on a several hours-long ride where you could be far from a trailhead, at altitude, etc.
Fuel (carbs). Getting tired? You might be in the early stages of bonking. Eat something. This is the one time that sugar is actually good for you.
Chapstick. There's nothing worse than dehydrated, sunburned lips while you still have hours to go.
Warm clothing. Surgical gloves, over or under your regular gloves, can make a huge difference if it gets wet and cold, especially on a long downhill.
Tire plugs can save you needing to give up and resort to a tube, if you run tubeless. Tire plug kits can usually be stashed in handlebars or the hollow crank spindle.
Spare sealant (single use bottle). I save this for long, remote rides.
Navigational help: GPS, map, compass, etc.
First aid kit.
TP. The extra gram or two in your pocket might turn out to be the most worthwhile weight penalty ever.