Aside from letting the warm air out of your home, old or bad caulk can cause paint to peel and can let moisture into the window frame, which can lead to wood rot.
Recaulking an old window isn’t difficult. You’ll need a caulking gun loaded with the right kind of sealer (ask an employee at your local hardware store for a recommendation), a putty knife, some paper towels or rags that you can pitch afterward and a steady trigger finger.
Source: Cure for the Common Cold Room
Photo via Dean in SF
Step 1: Clear out old caulk.
Photo via Wikipedia Commons