Man of Honour
There's a brilliant book called Tau Zero (fictional) which is about a near-lightspeed ship that ends up out of control and the consequent results.
http://en.wikipedia.org/wiki/Tau_Zero
As far as I'm aware (it's one thing that's in the book and something that people seem to forget) while you might not be able to get to lightspeed, you can get very, very close (forget about the percentages, unless you want to run into millions of decimals) - and the closer you get, the more the time dilation increases. I was under the impression that you could accelerate closer and closer to the speed of light, but never breaking it, but forever increasing the time dilation to ever higher levels?
Your acceleration would decrease at an ever-increasing rate as your speed increased, if my understanding is correct (assuming your engines maintain the same force). So you'd soon get to a state in which you are accelerating closer to the speed of light but by such a small amount that it's not going to matter in your time frame.