if a space craft can travel with no air resistance, why cant it continue accelerating to the speed of light?

For accelerating, you need to change your impulse. For changing your impulse in space, you need rocket engines, which burn fuel and eject the exhaust. There is still no alternative to rocket engines yet, even electrical thrusters are rocket engines. In Electrical thrusters (Also known as Ion thrusters), the electricity of the solar arrays is used for accelerating the fuel to high speeds, in normal chemical rocket engines, this acceleration is produced by chemical reactions. Nuclear thermal rocket engines use the heat of a nuclear reactor to directly accelerate fuel before ejecting it.

So, the maximum speed you can reach, is limited by the fuel you use, the effectivity of the engines and the amount of fuel you can put into your spacecraft.

Currently, we are already happy if we reach 19.6 km/s relative to Earth. And even the fastest probes, that ever buzzed through our solar system, the Helios probes, reached only 76 km/s relative to the sun. Not even one percent of the speed of light.

As a space craft speeds up, it gains kinetic energy. The problem is that E=mc^2, thus as it gains energy, it gets heavier. As that happens, the force is the same, so it acceleration decreases, and the spacecraft never crosses the speed of light. It can get really close however.

Others have noted the mass and energy problem correctly. To go the speed of light would require an infinite amount of energy...more than is available in the entire universe.

But your problems do not stop there! There is an issue with time as well. The closer you get to the speed of light the slower time will pass for you compared to someone in a different reference frame (not moving).

Remember you always measure the speed of light as the same speed no matter how fast you go. Since speed is measured simply as distance over time (e.g. miles per hour) the only way you can make the calculation work to always get the same speed of light is to adjust the time component (actually the distance component gets futzed with too...rulers get shorter the faster you go). If you are going as fast as the speed of light the time component becomes infinite.

Which is to say time will stop for you if you traveled at light speed. If you somehow managed to move at light speed (which you can't) you'd never do another thing till the end of the universe itself as you'd be frozen in place literally forever.

According to current knowledge, nothing can exceed the speed of light. That said, there exists the possibility that what we know may not be correct. At some future point, we may discover a way to exceed the speed of light in our universe.

While space is essentially a vacuum there are other factors that provide resistance, not the least of which is gravity from various massive and not so massive objects.

In theory, a small amount of force applied to an object in space for a sufficient period of time could accelerate that object to near light speed.

The many answers you got prompted me to respond...
First, they and you missed a main point. Space is not totally empty. At Earth related speeds it is nearly a vacuum. But there are gases and dust and various energy fields in space. So in fact at high speeds there is frictional resistance.

That being said, and for this question ignored, acceleration requires a change that in most cases occurs when energy is transmitted from one mass to another. This is the famous 'For every action there is an equal and opposite reaction' statement. It is commonly called thrust. And in a rocket this thrust is transmitted to the thrust plate at the top of the rocket chamber. The fire going out the other end is the opposite action.

Great. Easy to understand. Ok. Now zoom way in to the surface of the thrust plate. Atoms of energized gases transfer energy to the atoms of the thrust plate. How? By the interactions of the electromagnetic field lines which surround both the gaseous atoms and the thrust plate atoms. Basically the kinetic differences between the gas and the thrust plate become less and less as the thrust plate accelerates. At first the gas is moving at a high speed and the thrust plate is stationary. The energy available to accelerate the thrust plate is 100%. As the velocity of the thrust plate moves closer to the velocity of the gas - which is related to the gas temperature - the amount of energy which is available to accelerate the thrust plate diminishes.

In the real world, the rockets never approach this speed. In a solar powered ion drive they might. But there will never be enough difference between the heat available via solar exchangers and the thrust plate to reach the speed of light. The highest speed reached by reaction engines will be from those which collect light and direct it at the thrust plate directly. The thrust plate vaporization via laser stimulation offers a high percentage of the speed of light.

:-D The difference between normal reality and the speed of light is so great that in order to approach the speed of light via reaction thrust, both the fuel and the energy to heat it and use the heat for acceleration would have to be collected by the craft as it moves through space. The other alternatives are some kind of electrical/magnetic drive or the ultimate: gravity drive. There have been interesting electromagnetic propulsion systems which may end up in space craft. Nobody has a clue about how to control gravity. Some studies indicate that the speed of gravity might be 20 times or more the speed of light, all the way up to infinite speed. That is one reason they spend billions on the huge particle accelerators. If we can figure out how to make gravity work for us, then were really in the space-faring business.

there is still inertia in space, that is why there are theories of dark matter. it's why light takes 8 minutes to travel from the sun.

Dan -

The question you have asked reaches to the heart of Einstein's work on relativity. What he knew 100 years ago (that few people know today) is that the speed of light is constant, regardless of the motion of the source or the observer.

What that means in simple terms is that if you depart from our sun and travel at, say, 99% of the speed of light - then the light from our sun will still pass you - relative to you - at exactly the speed of light. If you are approaching another star at 99% of the speed of light relative to that star, then the light from that star will still pass you at exactly the speed of light relative to you. (ADDED: This has been demonstrated repeatedly in laboratory environments. There are distant galaxies that are moving away from us at 70% to 80% of light speed. Yet the light from those galaxies reaches us at exactly the speed of light).

So, if you travel anywhere, you will be leaving one reference frame that you may choose to use as your measurement reference frame. The light from that frame will always pass you at the speed of light. You cannot catch those photons. And it doesn't matter which reference frame you choose, the light from any (inertial) frame will also pass you at the speed of light. That's why there is no such thing as an absolute frame of reference that you can use to measure motion against. In a sense, you can apply as much thrust or power or solar wind to whatever craft you choose to construct, but after all your efforts you will be no closer to actually reaching the speed of light than you are today when you are standing on your front porch.

In order for this to happen, space and time have to undergo some changes, since space and time are what we use to measure speed, and since the speed of light remains constant. This is how relativity works, and it's how our universe works.

Simple - it takes energy to accelerate. With no air resistance, a spacecraft will travel at a constant speed unless force is applied to it. As you approach the speed of light, your mass grows exponentially, and it requires more and more force to accelerate you any further. It would require infinite amount of force to accelerate you to the speed of light, as your mass would also become infinite.