Don't get stuck by the side of the road! Obviously you can't take everything you might one day need on a ride with you, but a few basic tools can get you out of a lot of trouble.
As every rider and the conditions they face are different, there is no exhaustive list of what you must take on a ride. Over time you will get together what you need for your rides, unfortunately it will probably mostly happen by learning from your mistakes.
As a starting point, we would recommend carrying a pump with two spare tubes, and a repair kit just in case you need to fix several more punctures (a personal record is 7 on one ride). In addition, a good multi tool should cover a lot of mechanical mishaps.
Our most useful tips are try and choose a multi tool that includes a chain splitter, a broken chain doesn't have to end your ride, often you can remove a link and rejoin it so you at least have some usable gears. Also consider steel tyre levers, if your tyres are tight fitting then plastic or nylon levers can become brittle and break. This is a particular problem in colder weather, the worst time to have to walk home.