I've discovered that I'm really, really lucky. The art department at Llewellyn Publications (Flux/Midnight Ink) has tremendous talent and has been receiving much acclaim for their covers.
They sketched out a preliminary cover early in the production process and shared it with me as soon as they had the draft ready. The acquiring editor asked me my thoughts. I thought it was fantastic, and told him so. I would never have been able to envision the cover they designed. Plus, they had obviously spent a good deal of time reading through my book to even formulate the idea.
Apparently, though, other authors aren't so lucky. Agent Kristin on her Pub Rants blog delves into the importance of a cover consultation clause in authors' contracts, and what editors say and what they mean when it comes to covers.