I know I'm a little late to the conversation here, but I thought I'd give a little friendly information about the jumping spider mating dances as there was recently a program on in which they were mentioned, and I thought some of you might enjoy the info.
The male jumping spiders do a little song and dance routine for the females when they notice them. The dancing is the most obvious part (moving back and forth and moving those front two legs around in the air), but the "song" part is actually vibrations they make on the surface they're on at the time. Since they have no way of making vocal noises, male jumpers tap the surface with their legs and abdomen to produce patterns of vibrations for the female to feel. The more complicated and coordinated the movement and tapping are, the more likely the female is to like them.
They need to be careful, however, because if the female decides she doesn't like him, she may also decide to make a meal of him.
As for me, I love spiders, especially the little ones like jumpers. While I'm not fond of centipedes, I usually leave them be or "rescue" them also. Why? Centipedes subsist on a diet similar to that of spiders: smaller insects and pests around your house. If you don't want them crawling around your house, why not take them outside where they can eat pests without bugging you (or, if you have a colony of silverfish living in your house... you know).