Does pure water have more H+ ions than OH- ions?
No, if it's pure water then the concentration of both ions is the same.
Water undergoes what is known as autoionisation. Water can act as both a Brønsted acid (proton donator) or a Brønsted base (proton acceptor). This leads to the formation of
When autoionisation occurs it follows this equation:
So a mole of each ion type is formed per 2 moles of water. If the water is pure and contains no dissolved species that are also capable of forming these ions, then the concentration of both hydroxonium and hydroxide ions will be equal.