The ones which have a higher frequency than the plasma frequency of the respective metal... ;-)

From Wikipédia:

"Penetration depth is a measure of how deep light or any electromagnetic radiation can penetrate into a material. It is defined as the depth at which the intensity of the radiation inside the material falls to 1/e (about 37%) of its original value at (or more properly, just beneath) the surface."

However, metals are conductors. Inside a conductor in electrostatic equilibrium, the electric field is equal to zero. So, metals act as protect shields and block electromagnetic radiations.

https://en.wikipedia.org/wiki/File:Attenuation.svg

Electromagnetic waves contain oscillating electric fields and these fields can disturb the electrons in conductors and produce a penetration of an electric field into the conductor. This is called the skin effect. The longer the wavelength of the incident electromagnetic wave, the deeper the penetration. For example, the ocean is a good conductor due to the salt dissolved in the water. In the past, nations with submarines used extremely low frequencies (ELF, 300 to 3000 Hz) to communicate with their submarines. However the bandwidth was extremely narrow and very little information could be transmitted this way. A man-made transmitting antenna would be much too large, so they actually used the Earth as an antenna. Of course, the submarines could only receive data, not transmit back.

The ones which have a higher frequency than the plasma frequency of the respective metal... ;-)

Apparently, the refractive index of (bulk) matter, inclusive metals, tends toward 1 for sufficiently hard γ-rays. Accordingly, matter ceases to be sensible to radiations of highest frequencies, and becomes as transparent as air. Notice, however, that there are metal foams capable of shielding at those frequencies, too (https://www.sciencedaily.com/releases/2015/07/150717120323.htm).

A related question is if metals behave as mirrors in the whole frequency range below sufficiently hard γ-rays. As explained by dr. Akbi and dr. Redfern, thin metal films can be transparent also to radiations of lower frequencies. In addition, there is this claim: http://phys.org/news/2009-07-transparent-aluminium-state.html.

In fact, metals do interact also with light. For example, colloidal gold shows beautiful light effects https://en.wikipedia.org/wiki/Lycurgus_Cup.

I confined my answer to lower energy EM waves as i thought that was what the questioner wanted. Of course, at higher energy (UV) the photoelectric effect becomes important. Then there is Compton scattering and electron-positron pair production.

But, inside a metal V=0 for uniform electric fields. So, doesn't it mean no matter what the frequency is, fields will always grace the surface of a conductor? 

At high frequencies we have low Skin depth, and at low frequencies charges are always at the surface as electric field is uniform?

Or are these two separate phenomenons as one is described by JC and the other one by JD?

In ancient times the physical laws were stated without mentioning the associated domain of validity. Metals form a wide class of materials, and have different properties. Again, as noted by dr. Redfern, when speaking of γ-rays as electromagnetic waves, the conventions on the frequency range of electromagnetic radiations have been extended.

Suhas, when frequencies get high enough quantum effects become important. If EM theory were completely classical and metals were perfect uniform conductors, you would be correct. However, when frequencies get to the UV range, the particle properties of photons become important and you have the photoelectric effect, where photons have enough energy that when they deposit that energy in a metal it is sufficient to knock an electron out. At higher energies you have Compton scattering where a high-energy photon scatters off an electron. If a gamma ray photon of sufficient energy encounters the intense electric field in the vicinity of an atomic nucleus, its energy (E=mc2) can be converted into an electron and positron pair.

Subhas,

What Francis explained is correct. Moreover, even at low frequencies, you have finite depth of penetration of e.m. waves in metals because they are not perfect conductors with infinite conductivity. In fact, you not note how the skin depth varies with conductivity from any standard textbook on Electromagnetics.

The EM waves with longitudinal E component penetrate through the metal. In one experiment (http://arxiv.org/abs/physics/0010036), the authors used the metallic shield to be sure that they detected the longitudinal E field.

Exactly lesser the frequency it can penetrate easily. Actually theory is very deep but let me clear you in easy words. Touching on the base of theory, it depends on two things, 1) delta/lemda 2) delta/d {delta=distance between two particles, lemda=incident ray's wavelength, d=diameter of particle(not atom)}. Most of theories proved it depends more on delta/lemda than delta/d.

I'm telling you how, if delta/lemda is very law means imagine for same delta value ( compare to law lemda) ray may rarely hit the particle. As metal is made of particles. Electromagnetic ray can penetrate more in this metal piece. This is called dependent scattering and its critical value is 0.3, above this value its called independent scattering.