It depends on if you are using copper or aluminum wire. I prefer copper - it costs a little more when you buy it but does not have the issued aluminum can have down the road ... like needing to make sure the connectors stay tight if you weather goes from hot to cold on a regular basis.
If you are running 220/240 v line, you will need 4 wires. 2 hot wires, 1 neutral wire and 1 ground wire. For 200' you may want to run 2-2-2-4. You may be able to "pass code" with 4-4-4-6, but if you want to run a welder and compressor and maybe some heat in winter, you are better off with the slightly larger wire when running that distance. The ground wire can be smaller than the other three. If you run aluminum wire, you must use a larger gauge wire, use an anti-oxidation cream on the bare ends where they connect to the lugs and periodically check them to make sure they are tight ... copper does not usually have this problem.
Keep in mind that, with a sub-panel, the neutral bus should NOT be bonded to the ground bus or the breaker box case ... that is what the ground is for as the ground bus SHOULD be bonded to the case ... Also, it is usually good to drive a ground rod at your barn and connect that to the breaker box ground bus