Actually, scientists discovered that jumping spiders (cute lil things) have abstract memory, and are able to remember hazards they've previously encountered, as well as take the long way to their target if they think it would be safer. Which indicates that they at least have a rudimentary understanding of cause and effect, allowing them to plan. They also have great vision. There's a video of a jumping spider watching a helicopter overhead.

Having said that, jumping spiders, according to presently available data, seem to be along the upper edge of what "bug" cognition can do, and certainly smarter than the majority of spiders. Although spiders already tend to be fairly smart when compared to other bugs, such as flies.