How well can a helicopter handle someone jumping onto it while taking off?
The total mass of a light helicopter is about 1000 kg (depending on type and actual payload, of course). The 200 pound guy adds about 10%  to the total mass (and weight). The skids are relatively close to the centre of gravity (COG).

Immediate impact


Kinetic energy


In terms of mechanics, the jumping man will have a mostly inelastic collision with the helicopter, and he will transfer both, kinetic energy and impulse accordingly. One may simply choose the helicopter as reference coordinate system to calculate the resulting change of (vertical) speed for the helicopter:
$$\Delta v_\rm{H} = \frac{m_\rm{G} \Delta v_\rm{G}}{m_\rm{H}+m_\rm{G}} = \frac{1}{11} \Delta v_\rm{G}  \ \ \ \ \ \ (m_\rm{H}=1000 \rm{\,kg},\ m_\rm{G}=100 \rm{\,kg})$$
In the movie, the jumping man will just make it. The relative speed will be close to zero, and divided by 11 will be even closer to zero. If he had a significant speed relative to the skid, he would not be able to hold himself. 

The transfer of kinetic energy is negligible for the stability of the helicopter.


Added weight


The total weight of the aircraft increases by 10%. This sudden change creates a jolt which is clearly perceptible inside the helicopter, also suddenly changing the vertical acceleration. The (vertical) speed is the mathematical integral of the (vertical) acceleration. The speed will steadily change. The same holds true for the (vertical) position of the aircraft, which is the mathematical integral of the (vertical) speed.

In other words, the inertia of the bigger mass will prevent sudden  change of vertical speed. For the pilot, this 10% disturbance will be very obvious, and he needs to counteract. 

(Note that there was a related question recently: What would happen if a plane lost half of its weight instantly?)


Imbalance


The imbalance caused by the guy hanging somewhere else than under the COG creates a torque. This torque creates an angular acceleration. This angular acceleration integrates to angular speed, which integrates to roll and pitch respectively. While the angular acceleration starts suddenly, the angular speed can only change steadily.

The helicopter will not loose its attitude in a fraction of a second, like it happens in Hollywood movies.

Countermeasure

The pilot will use the Collective control to counter the added weight, and the Cyclic control to counter roll and pitch. Provided that the pilot reacts timely enough, it should be possible to stabilize the helicopter. 100 kg additional mass should not prevent the helicopter from climbing, unless it was already overloaded and without safety margins before the 200 pound guy arrived.

More critical is the torque created by the offset load and the resulting COG shift. I am not aware of the roll and pitch performance of small helicopters, but I believe that they are able to fly with somebody standing or hanging on a skid. Asymmetric load of this magnitude will likely impact stability and manoeuvrability, but will not necessarily cause a crash.

If the fearless 200 pound guy instead would jump and hold to the tail skid, the additional weight would be much further from the COG, and the outcome probably be disastrous.

Safety

This does not mean that it is safe to continue the flight with the 200 pound guy hanging anywhere on one skid. Pilots always need to verify if the amount and distribution of the load is within the performance limits of their aircraft. See "Helicopter - Weight &amp; Balance, Performance" for some explanation and example (note Figures 2-5, 2-6, and 2-7). Depending on the helicopter performance and the load distribution before the guy jumps, the new distribution may be within the specified safe longitudinal and lateral COG envelopes, or not.