wpegg: Exactly, for the very same reason you say they would need no acceleration. There is no resistance, nothing slowing them down, so nothing stopping them going even faster. There is no such thing as a top speed until you reach the speed of light, at which point you start getting into relativity and time dialation.
Breja: I... ok, I'm probably being an idiot, I'm no scientist. But you have an engine, and that engine has some max thrust it can provide. If it keeps pushing you forward with the same force, it won't make you go even faster.
You're not being an idiot, you just need to play Kerbal Space Program for a bit (it's amazing, really worth playing).
You said "you don't need to keep using up fuel to keep going in space. It's space. You won't slow down.". So in that situation, what if you used the fuel anyway and applied more thrust? Surely you'd speed up?
In "real space" thrust is cumulative, you don't lose any, you just add to it.
While we're back on the physics starwars obvious mess - have you ever considered that in space, in everything in starwars there seems to be a universal acceptance of "downwards"? I like to think there's a big arrow in space every so often pointing ships to which way down is :).