I recently been watching documentaries about the cause of WMD's, now, I'd like to give my opinion on the matter.
Now lets start off with America, obviously, America is well developed with high tech warfare, notable with the use of lasers, advanced weapons and unmanned drones.
The most serious effect would be a EMP or a Electro Magnetic Pulse. Why? The American army depends heavily upon electric equipments, radios communications would be cut off and the place would be scattered. Along as supports as aerial vechiles and electronic ground units such as Tanks which required electricity to run for most certain parts.
If it wear to be dropped on the heart of America could cause thousands of miles to be affected, not only that but as we all know the cables and transformers will be fried which will cause the equipment useless even if the aftershock of the EMP would be stopped.
In populated place like China would be devastating with "Germ Warfare", a biological weapon like "Q fever" easily spreads by just inhaling it, especially on a country like China with bustling streets. Yet a more infamous bio-weapon would be Anthrax, anthrax can survive the harshest conditions, it can be found all over the world, from the hottest places like Africa from the cold environments as Antartica. Anthrax is an "endospore", this kind of bacteria can live of to decades or centuries, and yes, there is a cure, but it will be too late when the disease are already spreaded out on different parts. In the Vietnam war, you must have heard of the "Agent Orange" which spreaded most on the corners of the country.
As you can see the most focused was on South Vietnam rather than the Northen Part, the program's goal was to defoliate forested and rural land, depriving guerrillas of cover; another goal was to induce forced draft urbanization, destroying the ability of peasants to support themselves in the countryside, and forcing them to flee to the U.S. dominated cities, thus depriving the guerrillas of their rural support base and food supply, in short it was part of a Unconvential Warfare
A third world country in most parts of Africa and mostly South East Asia would be a "Shock and awe" campaign, which is deliberately sending mass units into an area to demoralize or even break their will to fight, a third world country would be overwhelmed with the mass numbers and equipments and the invaded country would most certainly surrender if they were to prevent blood shed.
[As again, the would be my thoughts if it were to happen, before you mention things like "Well, can they drop a bomb with numerous countermeasures? Or can they do it with the countries back with the UN?" Again, these would only be my thoughts if it WERE to happen. You could post more info upon the controversy or correct my statements.]