To answer the question. I remember reading somewhere that they do bite but their bite isn't strong enough to pierce the skin and the venom is too weak to do any harm anyway.
Disclaimer - I can't vouch for the truth of that claim so it's best to be safe than sorry and nuke it from orbit, it's the only way to be sure.
House spiders were also taken internally to combat fevers. Richard Mead, writing in the 1700s, gave the prescription, ‘Take a spider alive, cover it with the new soft crummy bread without bruising it; let the patient swallow it fasting. This is an effectual cure, but many people are set against it. It has been frequently given to people who did not know the contents and has had the desired effect’ (Hillyard, 1988).
That spider from picture is brown recluse spider and can be deadly!
if you don't belive go and read about spider bites: spider bites
page brown recluse.
i know because i suffered brown recluse spider bite on my vocation..
i was in texas at my uncles home and spider bites me.
In first time i didn't know that was spider bite. After few hours pain was horrible and i decided to go to explore on internet some about spider bites.
Informations and pictures was telling to me that was really spider bite. I called 911 and went to hospital.
Doktor sad to me that brown recluse is so dangerous spider that can produce anputation, i was shocked!
That's my story people. I'm hoping i will help someone if read this and learn more about bites..
Sorry about mine bad english, i'm from bulgaria.
Make sure it doesn't bite you otherwise you'll start swinging from building to building with super spidey strength!

That plug hole is 3 inches wide!?!
Biggest bath I have ever seen.