Onsen have many different chemical compositions (depending on the area) and each onsen has a list of what ailments the water is effective against.
Many people swear by the effectiveness of the properties of onsen - whether bathed in or drunk (be sure to check if the water is supposed to be drunk first!).
Most onsen now have separate male and female bathing areas, but you can still find some that have mixed bathing - some require bathing suits and others not.
One problem to be aware of is that many onsen do not allow people with tattoos to bathe, so be sure to check this out with them first and avoid problems later.