Actually, in our case, we do, because we have an ejector pit that tosses the waste water up into the overhead sewers. So when the power goes out, we have to worry about things like flushing toilets and the like.
Or so I thought. After a careful inspection of the plumbing stack, it looks like the only water that flows into the ejector pit comes from the washing machine and the not-connected-to-anything plumbing rough out for a basement bathroom.
That's good news. I can get by without power for a lot longer than I can get by without a toilet. :)