How do you defeat the first spider in Limbo?
Run up to the spider, and just as its leg is about to do the stomp animation run back. Do this a few times and a bear trap will fall from a tree branch to the left. Push the bear trap to the spider and do the same thing you did before (wait for it to stomp and run away). Position the bear trap so that it hits the bear trap. Do this 3 times (against 3 legs) and you'll beat it.
Bara's got it right. Just remember that the third leg reacts rather quickly (far faster than the first two). I found out the hard way :/
Watch out for the third leg you snap in the bear trap - it goes faster than the other two and will get you if you don't back away early.