1) Torques are often mentioned in context of engine power and transmission gears. Engine manufacturers usually specify the maximal Torque (T) their engine is capable of producing. If you know the radius (R) of the gear attached to the engine, you can compute the force it exerts: T*R. Transmission gears along the way to the car wheels can increase or decrease this force. The following video explains that using the concept of engine power: http://www.youtube.com/watch?v=3-ilzx...
2) Many scales don't have a straight lever, but instead a downward bending lever. This produces the same effect of placing the points where the weight's forces are applied below the pivot, as explained at 1:37-1:55.
3) The video gives a visual definition of "cross-product". It is slightly different, though equivalent of course, than the traditional one. In particular, the vectors are placed one following another instead of placing both at the origin, and the right-hand rule is shown differently.
4) The last scene in space: this is a more general example since the object is not attached to a pivot, so it can arbitrarily move and rotate. The situation where there sum of forces is zero is a special one: In this case the object will not move but it may rotate, depending on the torques. Also special in this case that one may calculate the torques about any point (i.e., any point may be chosen as the pivot) and the torque vector result will be the same. From the symmetry of the object shown we now the true pivot will be in the middle.