Heh, reminds me of the old Critics United crew on FanFiction.net some years ago. Quite a few of them took great care of ripping your works to shreds, and called it "concrit" - well, while concrit certainly is most welcome, if one wants to improve, there sure are some borders the 'critic' should not cross. And the most active of those crossed every single one of them so much that they actually got an online petition against them.
Anyway - it really depends on the kind of negative. If people tell me my works sucks, and list what exactly sucks, and it's true, I actually thank them, since it gives me the much needed kick in th butt to correct things and actually improve my style. (although, if those people tell me my grammar/spelling sucks, and their own is not much better, there is only so much I can take seriously about their opinion. Always makes me laugh when someone calls themselves in all seriousness a 'Grammer Nazi' and then kicks their own grammar out of the window.)
If it's just some meaningless trolling, I mostly just laugh, think something about idiots who really should get a life and delete them.
And if it's negative because people do not agree with me on something - well, that's great. If everyone would always agree with everyone else, where would be discussion, where would be conflict that pushes us all forward?
As much as negative reactions can really depress us, I think that to certain degree we need those as well.
Like the latest comment I got from my betareader for one of my stories. I asked her for her opinion - whether she thought there was some issue with my writing that I would need to work on, did the story flow, or was it dragging itself forward at the speed of a turtle in peanut butter? The reaction I got was basically "well, it could have been much worse", and believe me, I was flailing hopelessly in front of my computer for about five minutes before I started laughing like idiot. I hoped for something a bit more detailed, but at least I know it wasn't commplete crap, even if it sure could be better :D