The more general formulation is E=GAMMA*m*c^2
Where GAMMA (known as the Lorentz factor) is 1/(1-(v/c)^2)^.5
Gamma is a dimensionless factor that depends on the ratio of the velocity of the mass divided by the speed of light.
As the velocity approaches c, GAMMA (and thus the energy) approaches infinity... In practical terms this says as you approach the speed of light it requires more and more energy to increase the velocity by a given amount. To actually accelerate any mass to the speed of light would take infinite energy.

This isn't just some abstract quirk of mathematics- this is real, verified countless times a day in particle accelerators.

The relativistic kinetic energy can be written as (Gamma-1)*m*c^2 (TOTAL energy minus the rest mass energy)... It takes a little math, but it is straightforward to show that when v<<c this reduces to the classical kinetic energy 1/2*m*v^2

Einstein's equations (in both Special and General Relativity) and their implications have been verified countless times and have been found to describe reality with extreme accuracy- much of our modern world has been built around those equations.

Which is why I find it odd that so many crackpots pick on Einstein and claim they have a better alternative to his theories...

It is not as if Einstein just wrote down random letters in equation form until he found a combination that happened to work out...
E=m*a^2
E=m*b^2
E=m*c^2 EUREKA!!!

No, he started with the reasonable assumption that the laws of physics must hold for all reference frames, and then looked at what that implied- he didn't CHOOSE how the equations came out, it was dictated by the universe, he just had the genius to figure it out.

He listened when the universe told him just how weird reality was- length contraction, time dilation- just imagine how alien and unbelievable all that must have been at the time... yet he had to accept it, and eventually everyone else did too- because the derivation was elegant, and had no holes in the reasoning... and most importantly, the experiments showed he was right.

23 pages that changed the universe as we knew it

As wonderfully accurate as it was, the theory of special relativity was incomplete- -- but given the indisputable accuracy of the theory of special relativity Einstein worked to figure what those few holes in the theory were telling him- this was a much more complicated task, and the results were even more bizarre in their description of reality... this was the General Theory of relativity- This filled in the gaps, and again- most importantly- has been verified countless times by experiment and observation.

The nature of reality it revealed was even more alien to our everyday experience- mass and energy affect the fabric of space and time...

Einstein did not disprove Newton, Einstein showed that Newton's laws were actually approximations that are extremely accurate on the velocity and energy scales we experience in everyday life. You can very accurately send a space probe to jupiter using only Newton's laws- General relativity likewise did not disprove special relativity, it expanded upon it.

It is probable - at least scientists certainly hope so- that there will be a more complete theory that unites General relativity and quantum mechanics, this theory will look very different than any that came before it- but we do know that it will not 'disprove' general relativity or quantum mechanics- it will show how they are connected.

There are a few contenders for paths to this larger theory, the one that I personally find most appealing based on my view of the nature of reality is Loop Quantum Gravity, but I am in no way qualified to evaluate any of the contenders based on their scientific and mathematical merits... its just too outside my fields of study.