Yes you can, but it is not always easy to do. The joists may not be perfectly spaced and you only have a 1-1/2 inch target for attaching two edges of the drywall. As well, the floor joists are often not perfectly on the same plane, with one or more of the floor joists being slightly lower or higher than the others.
That is why so many people put 1x3 or even 1x4 strapping on the ceiling. It allows them to shim the strapping out perfectly flat. It also allows for a perfect layout 16 or 24 inches on centre. In addition you get a 2-1/2 or even 3-1/2 inch target for those two edges.
The only remaining argument against drywall on a basement ceiling is that there are often many wires or pipes that you may need access to some day for repairs or modifications, and now you have to start cutting into your ceiling. Suspended ceilings take a bit more head room, but they allow for easy non-destructive access to the joist space above.