2016 Update: I updated the presacral series to reflect the new identifications of Evers et al. 2015 in their Sigilmassasaurus description. This has the effect of putting a stronger S-curve back into the neck, but it still leaves us with a hangdog angle for the skull. Interestingly, the neural spine morphology suggests the building up of axial muscles or nuchal ligaments (or both) along the back of the neck and front of the dorsal column, which is not unlike what Andre Cau has suggested for Spinosaurus, and would make it analogous to what we see in Deinocheirus as well (but on a smaller scale than either of those taxa).
I'm not seeing the extreme upturn in the neck that Cau has hypothesized for Spinosaurus, but there is decent flexibility in the base of the neck, and of course Spinosaurus is more specialized in other areas and might be in the base of the neck as well - though I'd tend towards being more conservative right now since we don't lack for extreme speculation regarding Spinosaurus these days.
2015 Updated: After nearly a decade and a half here is the overhauled skeletal. The overall proportions aren't all that different, but some of the details are. The midline crest has been moved back above the lacrimal, and I can now confirm that the odd downcurving neck seems to be a real thing, although it also uses some upwardly deflected almost cervicalized anterior dorsals to achieve it. The gray portion of the ilium is the part that was preserved as an imprint (i.e. there is no surviving bone from those parts) and so its accuracy depends entirely on the observations of the original excavators.
Original description: Baryonyx wasn't the first spinosaurid found, but it went a long ways in clarifying what these sorts of theropods looked like and ate. And it turns out they ate fish - although like modern crocodilians, Baryonyx almost certainly ate anything else it could get a hold of too (both fish scales and iguanodont bones were found in its stomach).