Between my roomate and I, we could collect enough hair during the week to make a wig. I try to vaccum everyday because I hate seeing hair on the floor or the sofa. And yes, during a shower more than a few strands always come off.
You would figure that eventually we would start running out of hair (read: becoming bald), since this has been happening for years, but so far we have not.
Don't worry, it's normal. Like someone said, only worry if whole chunks of hair start coming off or if you have visible bald spots in your head. But if you are concerned go to the doctor anyway.