How are forces on the landing gear reduced or compensated for at touchdown?
There are lots of forces acting on the gear at the point of landing. The best way to minimize loads on the gear is to land smooth (I know that sounds obvious). 

For what it's worth you do not necessarily want to spin up the gear before landing for a few reasons. First off you would need to spin up the gear to precisely (or at least very close to) the speed that the plane was going to touch down at. If you spin the gear up faster you actually will create a problem by accelerating the plane when it touches down. Spinning the gear up can also have a serious gyroscopic effect (since you now have a fast rotating mass) (see here as well) that will affect the handling of the aircraft.      

On top of that remember that in aviation it's often about cost. What are the costs to maintain a system that pre-spins the gear vs the cost of tires. Some times its actually cheaper and easier to make a part that wears out some what quickly and replace it often, then design a complex system that require maintenance and up keep.  

It appears that some devices for spin up have been looked into but the rotational inertia problem seems to be more of a concern than wheal wear. I would imagine that unintentional side loads on gear are a bigger issue and bigger cause of wear on the landing assembly. Keep in mind that the addition of an assembly like this also adds weight to the aircraft, and no one likes weight that is not needed. 

This is a great research paper on the topic that suggests (in their conclusion) a pre spin situation would see 1.07% of the wear of a static situation. They go on to state that that they used a simple linear approximation and only accounted for forces in one direction but it would seem that it is beneficial for the tire.

On a side note this article even suggests the tires can be remolded so even if the are replaced often it seems they are recycled a few times. 


  an A340 will complete roughly 6,000 take-offs and landings, calling for about 25 sets of replacement tires, each 1.30 m high and weighing about 200 kg. The tires can be remolded several times before they are finally scrapped.


In general, it's the job of the pilot to reduce the forces on the landing gear when landing. One of the best descriptions I have ever heard of landing is that the goal is not to land but to "transition". In other words what you really want to do is transition the load from the wings to the landing gear as smooth as possible, this will reduce the load on the gear. In some cases (short runway heavy plane) your landing may see more force on the gear. I have never flown a 737, but I can tell you that I can put a Piper Warrior down on a 7000-foot strip with out ever feeling that you have touched the ground.