Gravity sucks!
Sorry, couldn't resist.
Seriously, though: Gravity, defined as an attractive force between particles having mass, does exist. It's been proven both mathematically and experimentally. HOW it works is a problem, one which defeated Einstein. He tried to lump gravity and electromagnetism into a unified field theory, but wasn't able to make it work. One thing they are sure of is that gravity is NOT electromagnetic in nature. Magnetically and electrically neutral particles will attract one another. Even energy exerts a gravity field. As I mentioned in a different thread, Mercury's orbit is perturbed not only by the Sun's gravity, but by the mass equivalent of the Sun's energy output (E=mc˛).