Why is the Death Star shaped like a sphere?

Everything with mass has gravity between it and each other thing with mass. There's gravity between you and your computer, but it's too small to have any noticeable effect.

For the effect to be noticeable, at least one of the bodies needs to be big, and not too far away. For example, the earth is big enough to keep us on it unless you have a big, powerful rocket. The moon is big enough and not so far away that it causes tides. The sun is big enough to keep the earth in orbit.

Gravity can be calculated as a tiny constant multipled by the mass of one object multiplied by the mass of the second object divided by the square of their distance. F = G * m1 * m2 / r^2.

So the Death Star: "It's colossal, the size of a class-four moon". But how big exactly? Wookiepeedia says:

The first Death Star was 160 kilometers in diameter, while the second Death Star was 900 kilometers in diameter.

A recent Reddit post puts this into context:

The Death Star is not nearly as massive as you seem to think it is. In another recent Star Wars thread, I calculated a rough estimate of 6.777x10^17 kg, which is roughly 1 / 108,395 the mass of the Moon or 1 / 19,389 the mass of Pluto.

That said, it still has some effect on other astronomical bodies, but not a significant one. To give you some idea, given the mass I calculated above and a radius of 80km, it would have a "surface gravity" of 0.7067 cm/s^2 which is 1 / 1388 the gravity of Earth. If you weighed 180lbs on Earth and were to "stand" on the hull of the Death Star, you would exert a force of about 2oz.

Others point out that the ship had artificial gravity generators, it's mostly all aligned up-down decks, so the ship's own natural gravity wouldn't make any noticeable difference. Wookieepedia again:

The Death Star's interior followed two orientations. Those areas closest to the surface were built with concentric decks with gravity oriented towards the Death Star's core. Past this shell of surface "sprawls", the Death Star's interior had stacked decks with gravity pointing toward the station's southern pole.

Also from Reddit:

The Death Star uses massive inertial compensators in order to allow it's massive bulk to be moved about easily. Since inertial mass is equivalent to gravitational mass, the Death Star exerts a much smaller gravitational field than it otherwise might. It's still very heavy even with it's inertial compensators up, it just won't [knock] planets out of orbit.

Finally, for something travelling in the vacuum of space, shape doesn't matter as there's no wind resistance. Other ships need to land on planets and fly in their atmospheres, but not the Death Star which was constructed in space.