Almost none at all to none at all in an aquarium. A LOT if it's, say, dropped from a great height onto your head.
They're mostly zinc now I think (other metals besides copper), not much copper because the value for the amount of copper it takes to make a penny is worth more than the cash value, if that makes sense.
I once worked at a shop where someone went and dropped pennies into each and every saltwater display tank. I don't think that the smelted metal has the same properties as, say, a copper sulfate solution, but someone like the Subcomandante would be best able to answer that.