Why does the water level equalize in a series of tubes? Say I have a series of tubes (not the internet) looking like this, where w represents water:
|    |      | |
|    |      | |
|wwww|      |w|
|wwww|      |w|
|wwww+------+w|
|wwwwwwwwwwwww|
+-------------+

Why is it that if I put some water in either side, the water level changes on the other side until they equalize? Why does this work even if I put water on the thinner side? And why is it that when you tilt the whole contraption, the water level is still even, although slanted?
 A: In a liquid like water, the pressure acts in an isotropic way.
That being said, imagine a slice of water in the middle tube; what are the forces acting on this slide ?
The force exerted by the pressure on the left side, and the one on the right side.
The one on the left depends and the height of the water column in the left pipe. The one on the right depends on the height in the right pipe.
If you want equilibrium, both have to be equal. Therefore the heights have to be equal.

About the pressure: pressure has dimension of force divided by surface, in common units: $N/m^2$.
The column of water on the left pipe exert a force, due to its weight (gravity) that is $g \rho S h$, where $\rho$ is the volumic mass, S is the cross section of the pipe and h is the height.
But the pressure is $g \rho h$, thus independent of the cross section of the pipe. This force (gravitational) acts downward, but the fluid make it acts in an isotropic way, thus being directed from left to right on the slice of water (see above).

A good schematic explanation is available in hyperphysics.

Edit:
Altough the diameter of the left pipe is bigger, the force exerted on the "slice" of water is not higher because the pressure on a given infinitesimal volume depends only on the height of the column of water above it. Imagine two simple straight vertical pipes filled with water and with equal height, one with a large diameter and the other with a smaller. It is true that the force on the bottom of the big one is higher, but the pressure will be the same, because the force acts on a larger surface.
A: The short answer is: the system (after long enough time passes) wants to attain a configuration which is stable (we say the system is in equilibrium).
Now would the system be stable if one side had higher column of water than the other? Of course not, because the pressure at the bottom would be different between the two sides, introducing some forces. It is these forces which lower the height of the higher column and vice versa. Now, if the system were without any friction this would result in harmonic oscillations with water going up left column, then right, then left, ad infinitum. But because of friction, energy is lost in the form of heat when water moves and it pretty quickly attains a stable configuration.
Still, I suppose you should be able to observe few oscillations if you make the height difference really big.
The slanted case is completely the same. Applying above intuition about stability, it should be clear that the surface of the water must always be perpendicular to the gradient of the gravitational potential and the surface must be a level surface of the gravitational potential (otherwise you introduce some nonequilibrium forces). In homogeneous potential this results in a plane perpendicular to the direction to the center of the Earth.
A: Another way to think of it is to take the rule that the water wants to minimize its potential energy.  (This is a basic principle of statics.)  The potential energy is just the average height of all the water, times its weight.
If the water level were higher on the right, we could skim a little water off the top there and dump it on the left.  The water we moved would go down some while the rest of the water would stay at the same height, so the average level would go down.  Hence, it wasn't at a minimum before.  Only if the water level is the same everywhere is there no way to skim a little from one spot, dump it somewhere else, and reduce the potential energy.
Caveat: see comments on this answer for a little more explanation
A: water pressure increases with depth, from the surface straight down in relation to gravity, so the pressure is the same at the same depth, whether the tube is 6 inches wide or 1 inch wide. raising the level in one will increase the water pressure at the bottom. so water will flow into the other tube until the pressure is equal, therefore the upper levels will be even horizontally. tilting it does the same thing water will flow through the connecting tube until the upper levels are even horizontally.
