I keep two glass bottles filled with tap water in a small fridge in my bedroom. The tap water smells fine out of the spout. A few days ago I noticed that the tap water begins to smell bad after sitting in the bottles for a few hours (in the fridge or at room temperature, it doesn't seem to matter). This is a brand new behavior.
As an experiment I boiled some tap water and put that into the (clean) bottles for a few hours. Previously-boiled tap water begins to smell bad after a few hours too.
I have a well and everything's been swell for the past four years. I have a water softener which seems to be working fine. My pressure tank is fairly recent (a few years old). It has been (quite) a while since I've had the well checked or the water tested.