I've got an uninvited but not altogether unwelcome tenant on a dark corner of my basement. It's a spider; specifically a House Funnel Weaver, Tegenaria domestica. I call him Ed, even if it is a female.
Ed in his lair, in a dank intersection of concrete blocks behind my dryer. He's a bit of a celeb in the spider world, as a photo that I took of him last year made it into the new Division of Wildlife spider booklet (p. 15). That's right - last year. These funnel weavers can live a long time, and I first photographed Ed on November 29, 2009, and he'd been around for at least a month or two prior to that.
Chances are good that you've got a funnel weaver or two in your basement. They aren't particularly large, nor do they command a lot of space. Might just consider letting them be, as they'll pay their rent by dispatching less desirable critters.