Is rebar necessary on low load residential driveways?

Rebar or steel mesh is a good investment for a driveway. Local codes may actually control how you do your pour, have you pulled a permit yet?

No permit pulled yet. Local code would be Denver, Colorado and I don't know what that would be. Exactly why is it a "good investment"?

Well for starters if your code requires it you might waste a lot of money if you did not use it. Building codes often specify exavtly what they will allow and require. My local code allows mesh which is twist tied or rebar. When we do asphalt they actually come out and bore a small hole to make sure it is 2 1/2 inches before we roll it. I'd suugest calling the Denver building department and ask about their code and permit fees. City and County of Denver Development Services Looks like they follow the 2009 IBC

Depends on how you want it to last and what loads will be on it. Most driveways that I have seen built as part of road construction projects (when road changes disturb existing driveways) are reinforced with wire mesh, used primarily to resist cracking.
If oil, etc delivery trucks are expected to use the driveway, a thicker slab or reinforcement should be considered. On asphalt or concrete driveways, one truck can cause damage-it doesn't have to be sustained or frequent loads. The expected life of the driveway is also a part of the investment that ballenger spoke about earlier. A good well-drained foundation for either type driveway is essential also.