No I certainly do not overpay my mortgage and whenever this question comes up, I find myself getting very mad at Eddie Hobbs, who used to go around telling everyone to overpay their mortgage.
If you are already very rich, then overpay your mortgage. Most of us are not at all rich.
Like most mortgage owners, I don't have a big rainy day fund sitting in a bank account, so comparing savings vs lending interest rates is purely theoretical in the first place.
If I put all my money into my mortgage, however, i will inevitably need a personal loan sometime in the future, or run up a big credit card debt. Have you seen the rates they charge?
Keep your money. Pay at the agreed rate. If you are likely to need a personal loan in the medium -future, do not pay down your mortgage. Save that money for a rainy day.