Q:

What forces are involved in bending a freekick like that?

Look at this amazing, incredible goal (higher resolution at youtube).

What are the possible forces that can conspire together to make the ball bend like that?

A:

The simple answer is Magnus Effect. But there are two different techniques that is used in scoring freekicks.

Imparting spin on the ball by kicking the ball on the side. This is the conventional technique used by most footballers. Here is the most famous example of this technique. The spin of ball can makes it curve due to Magnus effect. In your video the player seems to be using outside of his foot to impart a reverse spin to confuse the goalie
There is a more recent technique called 'knuckling' the ball. This involves little or no spin. The player hits the ball as hard as he can trying to get it over the wall. The high speed and surface irregularities then cause turbulent flow around the ball due to which the ball can deviate from the straight trajectory in unpredictable ways. Juninho was a great exponent of this technique. Cristiano Ronaldo also uses this. It is a much harder thing to execute.

Here is a great video explaining these techniques. 

