My parents have a Tappan dishwasher. It's got to be at least 15 years old now, and it still works. I don't know if it's loud or quiet, but those are relative terms. My mom thinks it's loud, but she doesn't even like the sound of a small fan running at low speed. I, on the other hand, find something like an air conditioner to be rather soothing, providing it doesn't have anything rattling around inside.
It's probably an inexpensive model though. I might be looking for a dishwasher sometime in the not-too-distant future, but my price range would be <$200.