Does it matter what water source you use when watering plants?

In most cases it doesn't make a difference, but sometimes it can.  Where I live, the tap water contains a lot of lime, [hard water] and some plants don't like it.  There are some plants that don't germinate well in our water, but once growing, they do fine.  We are told to water our trees deeply once in a while to wash the excess lime  down from the surface.  

My neighbor waters his garden with untreated groundwater, and it does fine.  It's the same hard water, just not sanitized.  He doesn't drink it because it isn't safe to drink.  Probably washes his veggies before eating them.  He happens to have found an unregistered well on his property, so he uses it for the plants.  

tap water is fine.

Some plants don't really like a lot of minerals in their water. For example, Dieffenbachia (Dumb Cain) leaves will turn brown if you used hard water. A lot of plants don't care. It depends on the plant.