What size wire and breaker do I need to use to run from my panel in my house to a shed outside, 120' away. I just want a light and 2 120v outlets in the shed.

10-2 could allow 1 Good 120 Volt, circuit, 10-3 could alow 2 circuits both citrcuits on opposite phases and sharing the same neutral.

I personally would use 3/4 inch PVC, and maybe pull a switchleg for a light and/or even travelers to turn on and off light to get between the two at night?
And with a trench open, you could conside TV, Tel, Computer, Intercomm, Camera..

Use a 2 pole 20 amp if using the 10-3, and a single pole 20 amp if using 1 circuit.

Can I use a 20 amp breaker with #10 wire... I thought I had to use a 30 amp because of the wire size?

Not exactly; a 30 amp circuit requires at least 10 awg wire, and a 20 amp circuit requires at least 12 awg wire. The reason 10 awg wire was suggested is because of the 120 foot run, which would cause voltage drop. Since 10 awg is larger than 12 awg, there will be less voltage drop.

.. Therefore, 20 amp breaker with 10 awg wire would be perfectly fine.

Great... thanks