Going a slightly different direction from HDE226868, I'm going to design my ship to be as big of a sphere as possible. To do this, I'm going to put all of the living space on the outer surface of a big hollow steel sphere full of vacuum.
I'm going to have a lot more steel sphere, mass wise, per square meter than I will living accomodations on the outside of it, so my question essentially becomes this: how big can I make a hollow steel sphere before it is crushed by its own gravity? Now it's time for equations.
Gravity
$g = GM_{sphere}/r^2$
Where $g$ is acceleration due to gravity, $G$ is the gravitational constant, $M_{sphere}$ is the mass of the sphere, and $r$ is the radius of the sphere.
Mass of sphere
$M_{sphere}=4\rho\pi r^2t$
Where $t$ is the thickness of the sphere and $\rho$ is the density of steel.
Pressure on the sphere
$p = g\rho t$
This is a conservative estimate, since only the outermost portion of the sphere actually feels the full weight of its gravity. The actual pressure involves solving a simple integral that I don't feel like doing right now .
Stress
$\sigma = pr/2t$
This is the equation for stress in a thin walled pressure vessel.
Final equation
Putting this all together, we get:
$\sigma = 4\pi G{\rho}^2r^3t^2/r^2t $
Or, simplified and solved for $r$,
$r = \frac{\sigma}{4\pi t G{\rho}^2}$
Plugging in values for the density of steel (8000$kg/m^3$), the ultimate stress of steel (3,757,000,000), and G ($6.67408 \times 10^{-11}$), we get a total maximum size of around 70,030,000km, given a thickness of 1m. Our ship's radius is inversely proportional to its thickness, so we can make it bigger if we make it thinner.
Of course, our giant sphere-ship will only be able to lurk about in deep space. Tidal Forces (Differences in the force of gravity between one side of the ship and the other) would destroy it if it came close to a large body like a planet or a star.