Is any new water being formed on our planet?

Chris - The answer is yes, there is!

The process of, if we say, respiration - that's the best example, if you look at the metabolic processes that are going on in every single living thing on Earth - what we're largely doing is burning a fuel; let's take sugar, glucose, C₆H₁₂O₆, and we react it with oxygen (O₂), the products of that reaction are CO_{2 -} carbon dioxide - and, you've guessed it, H₂O - water.

What you've effectively done is you've rearranged some of the atoms in the sugar molecule, mixed them with some oxygen and you've made some water de novo.

So there is water coming out of that reaction, and, at the same time, you've got plants, which are gathering energy coming in from the Sun and they're using the process of photosynthesis to drive the reverse reaction; so they're taking carbon dioxide out of the air, they are mixing it with water which they've got from their roots, and if you take the CO₂ and the H₂O, and the energy from sunlight to drive the equation the other way, you then get - you've guessed it, C₆H₁₂O₆, you're back to glucose again!

So, although there are no new atoms being made on Earth [except by radioactive decay], there are nonetheless, new arrangements of those atoms - new molecules - so you are making water which didn't exist before by rearranging the atoms...