Should I put a moisture barrier under tile on a basement floor?
There are waterproofing/isolation membranes that can be painted on such as RedGuard and Mapelastic. They're coatings you paint on. 

Much cheaper and easier to use than sheet style barriers. The sheet membranes like ditra provide better waterproofing and isolation to prevent cracks which are important in areas with a lot of moisture like showers or slabs with cracks. 

Years ago when I tiled my basement with porcelain tile I used a penetrating concrete sealer that you just spray on. Haven't had any problems.