Spacecraft acceleration - How fast could one possibly go without disintegrating? Assuming we had a spacecraft that could accelerate up to 10% of the speed of light, what speed could be realistically reached without breaking its structure given current material science? Space debris can be ignored for this question.
 A: For reaching a final speed of 10% of the speed of light, the above answers are completely correct. Speed doesn't matter, acceleration does, and even then, acceleration only matters when different parts of your ship are accelerating at different rates.
But this is only true up to a (very hard-to-reach) point, due to the existence of the Cosmic Microwave Background (CMB). It turns out that the faster you go, the more likely it is that the protons in your ship undergo the following reactions with CMB photons:
$$p+\gamma\to\Delta^+\to p+\pi^0$$
$$p+\gamma\to\Delta^+\to n+\pi^+$$
Once these reactions start to happen, the Cosmic Microwave Background itself begins to destroy your ship. It turns out that the threshold energy for these interactions to proceed is on the order of $10^{20}$ eV per proton (this is a well-known limit in cosmic-ray physics called the GZK cutoff). Assuming your ship is on the order of a few hundred kg, corresponding to something on the order of $10^{28}$ protons, in order for this to happen, your ship would have to have a kinetic energy of $10^{48}$ eV, which translates to $10^{29}$ J. This is obviously an impractical amount of energy (i.e. you would have to annihilate roughly $10^{12}$ kg of matter and antimatter to get yourself to that speed, which is roughly equivalent to the mass of all the fish on Earth), and would require you to have a speed so close to $c$ that an outside observer would scarcely be able to tell the difference, but it does set an upper limit on the kinetic energy of your ship if we assume that the CMB exists.
A: It appears that you're asking if speed, alone, is enough to cause a vehicle to disintegrate. 
The immediate answer is that, in a vacuum, speed is irrelevant.  A vehicle traveling at 99% of the speed of light will not experience any stresses at all due to its speed.  
The faster the vehicle moves relative to the surrounding stars, the more cosmic rays and micrometeorites it will encounter per second, just as a car driving through a rain storm will hit more raindrops per second than a stationary car.  But a vehicle with the mass of a Tesla would hardly notice the effects, even if it kept flying through the cosmos for a million years at near-lightspeed.
A: Acceleration is very different from speed.  Yes, acceleration can cause stresses.  But your vehicle can get to any given speed with anything from a very low acceleration (like 1 km/hour per second) to a very high acceleration (like a million km/hour per second).  In the first case it takes one second to reach 1 km/hr.  In the second case it takes one microsecond to reach 1 km/hr.  As long as the acceleration is kept relatively low, the vehicle can just keep accelerating without damage until it reaches any speed you want.
