Dribble-free soup: serve the "goodies" and broth separately
First, strain the "goodies" from the soup (chicken, noodles, beans, etc.) and serve them in a bowl. Then, serve the broth in a mug, and let them drink it with a cut-down straw.
*Forehead smack of "why didn't I think of that?*
I was a bit concerned about the idea of warm soup going through thin plastic straws. Plus, much as my kids love using straws, the waste gets to be a bit much. Enter: stainless steel drinking straws! Pop them in the dishwasher (or clean with the included brush) and reuse.