Max rocket speed in interstellar space? Interstellar space propulsion...if a spaceship were to get beyond our Sun's gravitational pull and since there is no atmosphere/wind/friction in space...does that mean, if an engine was constantly thrusting, that the spaceship would continue to accelerate to the speed of light, as long as the engine was propulsing forward?  In other words, does speed constantly increase in a vacuum? or are the two ideas (Space/Vacuum) separate ideas?  
 A: The answer is no, according to Einstein's Theory of Relativity.

As an object approaches the speed of light, more and more energy is needed to accelerate it further.  To reach the speed of light an infinite amount of energy would be required. 

Also, there is wind/friction in space. There is no absolute vacuum, there is an interstellar medium. Indeed, relativistic rockets would have to account for the medium, and perhaps even use it as a source of fuel, see: Bussard Ramjet.
A: You asked three questions...
1.) ... does that mean, if an engine was constantly thrusting, that the spaceship would continue to accelerate to the speed of light, as long as the engine was propulsing forward? 
No. For reasons ghoppe gave.
2.) ... In other words, does speed constantly increase in a vacuum? 
Yes, speed would increase continuously, for the example you gave, asymtotically approaching (but never reaching) the speed of light.
3.) ... or are the two ideas (Space/Vacuum) seperate ideas? 
No.  A vacuum is an excellent and practical description of what most space is. 
A: Assuming that our perceptions of Relativity hold up in interstellar space...
The ship would continue to accelerate as long as fuel held out. 
Speed would continue its asymptotic clime towards C... 
until drag was sufficient to end that climb. Drag would also increase due to interstellar medium collisions as speed increased. But note also: a sufficiently high thrust will not be exceeded by drag.
Note that as speed increases, and drag increases, so does radiation. The interstellar medium results in Alpha & Beta radiation increases, and high energy photon releases from same producing X-ray and even gamma radiation.
Note that several science fiction works have relativity have a cutoff point. In a few more, Relativity is ignored entirely; the most egregious offender is E.E. "Doc" Smith's Lensmen series. John Ringo's Looking Glass series has heliopause boundary changes to the nature of physics, including relativity
A: A rocket-powered vehicle is always going to be limited by its own propulsion system.
If we assume infinite fuel loads [plus a bit more for the rocket] then intuitively we can see that if all of the fuel is instantaneously expelled at the speed of light, the rocket can exceed the speed of light (if we ignore relativistic effects for a moment.)
However this is impractical - the fuel will always take a finite amount of time to burn, so during that time it also has to propel the remaining fuel, i.e. on average half of the thrust is used to accelerate the rocket, and half to accelerate the fuel, giving a practical limit of half light-speed, and that is assuming perfect combustion, which is itself not realistic, even with Newtonian physics.
