Before I stumbled upon doing the phlebotomy (blood-draw) thing that I do now, I was all geared up to get into mortuary science. Main reason I decided against it wasn't the whole dead body issue, but rather the employment one: how often do you see ads for "mortician wanted" in the paper? It's really hard to get started in the field because it's all about who you know and whose arse you kiss to get in there.
The gore, itself, doesn't bother me, really ... kinda fascinates me in a morbid sort of way. I've seen a few dead or soon-to-be-dead bodies over the years. An uncle at a wake when I was too young to really remember; one old lady that got run over by another old lady in front of Wal-Mart (heard a thump, turned and saw a crumpled up ol' lady on the ground, she died within minutes); drove by a gory accident scene or two where they were peeling people out from within twisted wrecks.
I come across cadavers at least once a week, now. The laboratory of the hospital I work at is right next door to the morgue, so every once in awhile when you're coming off the elevator and heading that way, you pass by a dude carting along a body on a gurney with a sheet over it - nothing graphic, usually, because it's usually just old people that've kicked the bucket due to ... well, just being old. Really, seeing trauma patients come in through the ER doors or being unloaded from a medical chopper is more disturbing to me than a dead body - those people are still alive and suffering, and maybe SOON to be dead.
As stated, the trick to dealing with the sight of death is that, aside from witnessing the actual moment of a person's passing from life, you have to look at a dead body as an IT, a THING, or an inanimate object - the spirit/soul/whatever that was within that body before has already passed on, so all you're looking at is a pile of meat n' bones. (Sad to think that's all we really are in the end, but that's about the sum of it.)
The actual moment of a person dying, on the other hand, is kind of a heavy deal - seeing a person go from being, well, a PERSON in one moment ... and then only being so much meat n' bones. Gory death or not, the change from someONE into someTHING is just bizarre, which is probably why death is probably one of the all-time most fascinating subjects throughout human history.