This is a tricky question.
I'm squeamish in that I don't like watching the news. I hate how they show people being wheeled away on gurneys, because I always think what if someone's sitting in a bar or something and they look up and realize they know that person? I don't like when they show the skycam footage of the accidents on the interstate, even though it's low on actual gore, and I particularly hate hearing that terrible things have happened to children or animals.
The flipside is, if it's from a scientific point of view, I have no problem. I've always loved anatomy and dissection. Every time I've had surgery, stitches, or an IV put in, I've been very fascinated by the process. I like to watch them take blood. I have some titanium pins and screws in my knee, and before they went in, I unnerved the orthopedic surgeon by asking if I could hold them to see what they were like (he was very obliging).
I also have a weirdly high threshold if it's part of my job. For a while (five years), my day-job was as a lab technician in a photo shop. Eventually, I wound up being the exclusive handler of the district crime scene account for the police department. It was assigned to me on the premise that I had good attention to detail, and admittedly, there were a lot numbers to write down and special instructions to follow, but mostly, I think I got it because none of the other girls wanted to deal with it. It was bad sometimes--I won't deny that. In theory, I always knew that the human body has a lot of blood in it, but it's different seeing it all over everything. Still, I could always do the job, and mostly found it interesting.
Elincoln asked about actual bodily fluids, and as far as that goes, I'm pretty impervious. In high school, I wound up being the drunk-sitter by default a lot of times because vomit doesn't really bother me. I mean, like any rational person, I prefer to avoid it, but it's not intolerable. The same goes for blood. In the ninth grade, I had health teacher who'd been in Vietnam. He was obsessed with first aid and violent wounds, and so we spent the whole quarter looking at pictures and learning the patch people up. Once, when we were looking at color plates of dog bites and compound fractures, my desk-partner passed out and I got to treat him for shock.
Yeah, I'd have to say that oddly, gore bothers me less when I'm somehow involved than when it's completely removed from me and I can't do anything about it.