Me, I draw the line at organs, period. I just don't like seeing them, even when they're clean and neatly packaged at the store (bleck). I remember that B99 episode where they faked Pimento's death and used baked beans to represent his splattered brains (XD)...even that was pushing it for me, when I didn't know it was coming.
The only place I can stand organs is (oddly specifically) anatomical drawings, like for educational purposes. I guess maybe there's a feeling of detachment, seeing as (a) they're not really photorealistic, and (b) you don't have a sense of them 'belonging' to anyone. I dunno.
When it comes to blood, though...make it rain; I don't really care. ^^ It's the other aspects of violence (the screams, the fact that a character you care about is in danger) that make me upset; blood alone doesn't really do anything to me. Like if two competent characters (or characters I'm otherwise not worried about) are having a bloody battle to the death in a manga or something, I could read that for days. It's exciting~
For that reason, I always want to have blood or a blood analog in my more violent stories. In fact, I'm working on rewriting a story with a dead protagonist, and the fact that he probably won't be able to bleed is kinda making me sad...