I have a typical house plant growing in a antique clear glass vase. Lately I have been needing to change the water almost every day, because so much algae is growing on the inside. Is there anything I can add to the water to stop the algae growth, but not harm my plant?

If you are changing the water every day then there is no harm in changing the receptical and cleaning the old one thoroughly. By the way, why do you have it growing it water?