There sure are a lot of spider- and insect-shaped things on Mars. Yll reads books that talk about ancient men carrying "clouds of metal insects and electric spiders into battle" ("Ylla," 1). The little girl in "The Earth Men" plays with a "golden spider toy." Muhe Ca rides a vehicle that looks like a "jade-green insect, a praying mantis" in "Night Meeting."
Oh, and don't forget the "golden, horrid bees" that Yll uses to kill the first two men on Mars in "Ylla." Yikes!
So, obviously, spiders and insects can be good or bad (toys are good, weapons that kill people are bad). But the fact that the Martians design tools that look like creepy-crawlies indicates how different they are from humans.
Fun fact: the creepiest aliens always seem to resemble bugs: think Ender's Game, the Borg hive-mind, or, you know, Men in Black. (The awesome original one, of course.)
Spiders and insects seem to tap into a primal fear for Bradbury: this is as foreign and strange as he can imagine. And when you think about the way that ant colonies and bee hives work—the weird, almost telepathic communication they use—it makes sense that Bradbury would use them as a symbol of extraterrestrial life, since the good guys in his stories are always people who chose to be different and to break away from conformity.
(We'd say there's no "I" in insect, except, well, there is.)