This is most likely a long-bodied cellar spider (Pholcus phalangioides; additional images), and depending on your geographic location, is also known as a daddy-long-legs, a vibrating spider, or in Britian, sometimes a cobweb spider. (Some of these names can really confuse people, because one name in one location refers to one spider, where in a different place, the same name refers to a completely different critter.)

So the answer to your question is: depends on what you want to call it. ;)

Note: There is also a family of spiders called "cobweb spiders" or "cobweb weavers". This family (Theridiidae) contains the common (or American) house spider, false widows (Steatoda), and widows (Latrodectus). These spiders are completely unrelated to the spider in this image.


"Your" spider is not dangerous to people, and is encouraged to build around (and even in) your home, as it is great in catching little insects that can be a nuisance or a pest (e.g. - little fruit flies, ants, etc.)