On the large scale, gravity is much stronger than electromagnetic force. But in what cases was the electromagnetic force stronger than gravity on the large scale i.e. objects of the size of the Earth, Moon, Sun, etc? Put in another way, what are the largest objects ever to experience an electromagnetic force stronger than the gravitational force?
BTW, this question was inspired by What is the smallest item for which gravity has been recorded or observed?
The problem with large charged objects is that they quickly neutralize themselves; for instance, the most massive charged objects that theoretically exist are charged black holes which obey something called the Reissner–Nordström metric. However, as the universe is neutral, and the electromagnetic force is very strong compared to the gravitational force, these black holes quickly neutralize themselves and we effectively never see them. Also taking into account that charged objects the size of planets as you ask must necessarily be extremely far away, it becomes difficult to measure the charges of such objects (especially when compared to measuring their masses).
"what are the largest objects ever to experience an electromagnetic force stronger than the gravitational force"
Answer is: everything except black holes and neutron stars.
That is, the internal interactions which prevent things being crushed under their own gravity are largely electromagnetic in nature, though admittedly the size of atoms comes about also via the quantum mechanics of position and momentum.
But I guess you really wanted a more cumulative effect; for that, see the other answers. I note that electromagnetic fields in between stars are weak but spread over large volumes, so that they can easily be the dominant influence on charged matter in those regions.
It is not obvious that, say, two charged neutron stars cannot interact with Coulomb forces larger than gravitational forces. For example, authors of article http://www.if.ufrgs.br/hadrons/MMalheiro.pdf consider charged stars and note: "If these highly charged compact stars exist, they need to be isolated systems since outside the star, the Coulomb force will overwhelm the gravitational one."
