Have a look at http://physics.stackexchange.com/questions/80807/why-do-same-opposite-electric-charges-repel-attract-each-other-respectively for an explanation of the attraction between charges (I'm using the word *charge* in the general sense). It looks long and intimidating at first glance but persist because it isn't really.

For there to be a gravitational repulsion there would have to be negative mass e.g. some object with a mass of -1 kg. Note that this is not the same as antimatter - antimatter has a positive mass just like normal matter. We have never observed any matter with a negative mass, and as Chris notes in his answer negative mass would violate all sorts of conservation laws so it probably doesn't exist.

See http://physics.stackexchange.com/questions/44934/does-matter-with-negative-mass-exist for a discussion of negative mass, or [this search][1] for more on the subject.


  [1]: http://physics.stackexchange.com/search?q=negative%20mass