Dear computer-gods, please explain why some airplanes have wings that go straight across, some angle upwards, and some angle downwards? Why isn’t one style best?
The first thing you have to understand is that a positive dihedral (a wing that angles upward from the fuselage) creates roll stability – in other words, it will make the plane less inclined to roll to the left or right. The physics behind this so-called "dihedral effect" is complicated, but the basics are fairly easy to visualize; a positive dihedral moves the overall center of lift a little higher, placing it closer to – or sometimes above – the aircraft’s total center of mass. Effectively, with enough dihedral effect, the weight is hanging under the force that’s holding it up (as opposed to balancing on top). 

As you might expect, this sort of stability is often beneficial. You don’t typically want your airliner or cargo plane to flip upside-down, after all. But there are reasons to angle the wing the other way. 

Oftentimes, when the wing is mounted high, the center of mass is already far below the center of the lift. This can make some roll maneuvers excessively difficult. A negative dihedral angle (often called an anhedral) can reduce this roll resistance to more reasonable levels. Many military cargo aircraft, like the An-124 and C-5, are designed this way.

Some planes are built with a dihedral angle that intentionally reduces their roll stability. Though it sounds counterintuitive, fighter aircraft are most maneuverable if they are at least slightly aerodynamically unstable. The proper dihedral angle can help them hit the right balance between stability and instability.