You can definitely brew green tea in a pan or even a bowl or big pitcher or something, but you do NOT want to do the actual brewing over the stove! Green tea should never be brewed with boiling water (it should be around 175F, i believe) so what I would do is boil the water on the stove, wait 5 minutes (or just take it off the stove before it starts boiling), then pour it over your tea and let it steep for a couple of minutes. Also, never ever use a tea ball type thing with green tea - it compacts the leaves too much. If having leaves floating around bothers you (I just make my tea directly in the mug with leaves floating around.. but I am Chinese and used to it, having drunk it that way all my life...) you can pour it through a strainer after it's done.
The Zojirushi water heater that Janet posted is excellent - I do not have it, but my parents and other relatives do - in my family, what we do is everyone has their mug with green tea leaves, and it gets constantly refilled throughout the day from the water heater. A good thermos (like the camping kind that keeps drinks hot for hours) works too. You can resteep the leaves several times if it's good tea!
