I have been riding trails on my mountain bikes that are tubeless so I haven't patched or changed a tube in a long time. That said when riding with tubes I typically change the tube and patch later. Depending on the situation I may carry 1 tube or 2.
Also sometimes if the location of the puncture is obvious without taking the tire off I may sometimes leave the wheel on, break the bead on one side part way and pull out just enough of the tube to patch it with the wheel still on the bike. That can work out when there is an obvious thorn or other offending object that can be located and removed without removing the tire.