The most that happens is Zero, a robot, blowing himself up and losing the lower half of his body. There is also something resembling blood coming out of his mouth in his portrait when he's talking to X as he's dying. It isn't excessive, per se, but it does exist.
SPOILER: in the first game, a character sacrifices himself to help the protagonist and is assumed to have died. However, in X2 you can find his pieces and put him back together, reviving him