First, it's important to distinguish what kind of energy you are talking about. In this case, it seems we are talking about potential energy. In the case of charges, the potential energy is a way of describing the force acting upon the charges due to mutual attraction or repulsion.
Generally, potential energy is a relative scale, i.e., it is only defined relative to a point of reference, which is assigned a value of zero. For point charges, that frame of reference is when they are infinitely separate. Therefore when the distance separating two point charges is infinitely large, they have a potential energy of zero.
In, say, a hydrogen atom, as the electron gets closer to the proton nucleus, the potential energy is smaller. This is consistent with the fact that the charges are attractive because they are opposite. A system moves toward lower potential energy if possible. Note that lower potential energy does NOT mean closer to zero! It means more negative.
This is not in disagreement with the coulomb potential equation, because recall that the equation includes the electric charges. So, as r gets smaller, the magnitude of the potential gets larger, but the sign is negative (positive nucleus * negative electron = negative value), so the potential energy gets more negative, i.e., smaller. If r = 0, the potential energy is undefined, negative infinity.
One of the peculiarities of quantum mechanics is, of course, that the electron does not fall into the nucleus, even though classically it should (like an asteroid falls to the earth). Only certain values of r are allowed, determined by the quantization of the energy eigenvalue.