Jumping spiders are among my favorite animals.   They look (and behave) like they're full of personality -- highly visual and alert, active, and seemingly unafraid.   They're aggressive predators that act like big cats: stalking prey and attacking in a leap or a rush, then biting and wrestling it into submission (sometimes they go for insects much bigger than themselves).   This one is Phidippus octopunctatus; as far as I know there is no common name, but I googled a Japanese blog with photos of this species and the English name 'giant gray mouse-eating jumping spider'.  That seems rather ambitious for an animal that is about a cm long, although it does have startlingly big fangs.   Females are grayish with large abdomens; males are strikingly black and white, like little pandas (or skunks).  In one photo a male is displaying with his long forelegs; I think he saw his reflection in the camera lens.   These spiders came from near San Diego, California (I took the pictures in my lab at the University of California, Riverside).
            Images of other jumping spiders are here, here, here, here, here, here, here, and here.