There aren't enough video games that let you play as a spider. The only ones that come to mind are Spider: The Video Game for the PlayStation and Deadly Creatures for the Wii. Fortunately both are quite good! =)
Great replies everyone! I was just thinking about console games on physical media, but it looks like there's a lot of really neat spider games out there for PC and mobile platforms too. And I had forgotten about the arcade game Black Widow! That was a great one!