For a standard 20-amp branch circuit, the usual choice is 12-gauge copper wire. That is the common setup for receptacle circuits and general-purpose 20-amp runs in most homes. If you are using copper conductors and the circuit is protected by a 20-amp breaker, 12 AWG is the typical match.
That said, the right answer is not just about the breaker size. You also need to think about the conductor material, the length of the run, and what the circuit will serve. Aluminum wire is a different story and is not normally used for typical 20-amp residential branch circuits in the same way copper is. For most DIY and residential work, people are talking about copper, and for copper, 12 AWG is the standard for 20 amps.
If the circuit is a long run, voltage drop can become an issue. For example, if you are running power a long distance to a detached garage or workshop, 12 gauge may still be code-compliant in many cases, but it may not be the best practical choice if the load is sensitive or the distance is excessive. In those situations, upsizing to 10 gauge can help reduce voltage drop. That does not mean you put 10 gauge on a 20-amp breaker because of the breaker rating alone; it means you may choose a larger conductor for performance reasons when the run is long.
Another thing people miss is that the entire circuit has to be matched correctly. The breaker, receptacles, splices, and wire all need to be rated appropriately. A 20-amp circuit should not be built with 14-gauge wire, because 14 gauge is normally used on 15-amp circuits. That would leave the wiring underprotected if the breaker allows more current than the wire is designed to handle. The breaker protects the wire, so the wire size matters just as much as the breaker size.
If you are feeding a specific appliance or tool, check the nameplate and installation instructions. Some loads have their own requirements, and some codes or local rules can be stricter than the general rule of thumb. It is also worth checking how many outlets and what kind of loads you plan to run. A garage circuit for power tools may behave very differently from a bedroom receptacle circuit.
So in most cases, the answer is 12-gauge copper wire for a 20-amp circuit. If the run is unusually long or the application is demanding, consider whether a larger wire size makes more sense. If you are unsure, it is smart to confirm against your local electrical code or ask a licensed electrician before you wire it up.