chaadster provided a most excellent list!
It should be noted however that there are more than a single school of thought on some items. One... is whether to carry a pump in your flat kit or a C02 inflator (uses a C02 cartridge to inflate the tire). Pumps never run out of charge.... but require LOTS of effort and time.
Some cyclists prefer not to use a saddle bag choosing to stuff tire repair items and such in a cycling jersey or strapping them to the seat post. Most select a smaller saddle bag. But even the very large bags get sold.... so someone must be buying them.
Phone protection should be mentioned. I think most of us use ziplock baggies. They are water (and sweat) proof. So my phone and few buck/dollars goes in a baggie before every ride. Getting caught in a cool rain on a hot day can almost feel good... when you know your phone isn't getting ruined.
Identification. Some carry wallets... with all the content. Some also or instead of wear ID bracelets. I carry a homemade laminated photocopy combo driver license and health care/insurance card.