There's no blood and gore anywhere in this movie, but it does have some violence. Magneto (the villain) seems to, in a way, torture Wolverine sometimes, thus taking advantage of Wolverine's valuable metal-coated bones. The most violent scene is when Wolverine accidentally stabs a girl through the chest. No blood is shown, but you see clearly his claws protruding right through the girl's back. This scene doesn't last very long, though.
Another somewhat agitating scene, is when Wolverine starts to remember his surgery to insert the metals into his body. Although this isn't anywhere near explicit, it could be a little scary for younger kids.
So 10 year olds would probably be okay watching this movie.