Given e=mc2, why aren't light particles infinitely massive?

Given e=mc2, why aren't light particles infinitely massive? Since mass approaches infinity as it's speed approaches light-speed. This according to Einsteins theory of relativity. Thank you in advance for your reply.
I gather from the two replys that light particles are massless or mass=0. Since light is a form of energy, and energy is a form of mass how can it then be considered to be zero? That still appears to be a an additional pardox.
Thank you Ozoneguy for the equation as it relates to a photon. According to Einstein energy and mass are both but different manifestations of the samething. Mass can be converted to energy and vice versa. http://www.youtube.com/watch?v=CC7Sg41Bp-U&feature=youtube_gdata_player I realize this is e=mc2 which you say should not be used for light particles.
@OzoneGuy it appears by =/= you mean not equal to. Since I don't recognize it as a universally accepted math symbol. Not that I know them all. Also I understand that you say mass and energy follow different laws. If, as Einstein states are different manifestations of the same-THING. What is the THING?
That is to say mass & energy are both but different manifestations of the same-thing. What is the thing?  IPhone typing on this small screen can be challenging at times.

The limit of x * 0 as x goes to infinity is still 0.

E = mc^2 is the formula for the rest energy of a massive particle.
The correct formula when wanting to include photons (which have no mass) is:
E^2 = (pc)^2 + (mc^2)^2
... where p is relativistic momentum, a vector.

Mass does not change with speed, despite what some textbooks still present today.  Relativistic mass changes with speed, and is a different value depending on which direction you might wish to accelerate the mass further.  What is most common usage is:
mass = rest mass = inertial mass = gravitational mass =/= relativistic mass

Energy is not a form of mass, but mass is a form of energy.  So more clearly, all forms of mass are energy, but the superset of energy has forms that have no rest mass.  That light has no rest mass is the result of theoretical prediction (I believe it would end up violating conservation of charge),  And we have tested photon's mass, and no rest mass was found at least 18 orders of magnitude smaller than its energy.

Paradoxes are just places where our "common sense" bumps up against Nature.  We make assumptions about how She works, based on very large collections of particles, at very low speeds, a very narrow temperature range, and for an exceedingly short period of time.  Our "common sense" is just a way of us ignoring how She works in some realm of experiences.

[EDIT: "Mass can be converted to Energy, and vice versa."

Yes but this does not mean they are the same thing, or the same laws apply to each.

The really cool part of the equation I gave you is that it can describe the total energy of a system of particles.  When that system includes for example just two photons that are travelling in different directions, say from a nuclear decay, THE SYSTEM has a non-zero rest mass.  The photons themselves have no rest mass, but the system of particles do.  What is more, THE SYSTEM propagates at less than c...  And that too is very enlightening ;>)]