The Rock, Paper, Scissors of Kings of War

You gotta hand it to them...they're on point.

Medieval warfare was often summed up by the tactical application of certain troop types being matched against another. In a very broad sense, a good approach to wargaming with fantasy/medieval units can be applied the same. While we have more fantastical elements in Kings of War (Dragons, Monsters, spellcasters,) the general feeling applies.
When we think of their effectiveness some units shine in certain situations more than others. This is all I mean when I say they have a rock-paper-scissors attitude. Note that this is not a discussion on movement, placement, deployment, etc. Purely A to B match-ups. It is also not the only solution for any of these, just general counters. Here are some examples:

Ranged units deter Fast units

Having some ranged attacks to throw into units such as cavalry or any other high speed target becomes appealing. They want to get to you as fast as possible and as healthy as possible. Even if you don't remove the unit from the board, putting damage on them counts in the long run. Anywhere they can run, you can reach them.

Basilean Crossbowmen

Fast units shut down Artillery

Artillery is stagnant and getting to it quickly is key if you want some of your more critical units to survive over the course of the game. Critically, don't throw the farm at artillery. Even individuals treble their attacks against them. They go down easy.

Gargoyles

Artillery stops Ranged units

Ranged units are also stagnant. That can make them hard to get to. With long ranged fire you can put the appropriate damage on these units to get them off the board over the length of the game. (A Mounted Hero of some sort is also a phenomenal way to shut them down.)

Goblin Big Rock Throwers

Light Infantry can attack Heavy Infantry and Defend against Light Cavalry

Light Infantry is often cheaper than heavy and is very versatile. In hordes, they can be a great tarpit for Heavy Infantry to lose their effectiveness in. In Regiments and Troops they can be wonderful deterrents for Light Cavalry that they actually outclass in combat effectiveness.

Orc Ax Horde

Heavy Infantry stops Heavy Cavalry

Kingdoms of Men Heavy Pike Block

Heavy Infantry is Infantry that is armed better with higher defense or special rules such as ensnare and phalanx. Any player looking to charge a unit like this hates to do it. A careful general makes it the only option to BE charged.

Light Cavalry pesters Heavy Cavalry and Heavy Infantry

While these units are never hammers, they can keep up with Heavy Cavalry and throw much needed points of damage into them with ranged attacks.  They also threaten any exposed flanks with their speed and make it very hard for Heavy Infantry to properly face a charge from Heavy Cavalry.

Elf Silverbreeze Cavalry

Artillery stops Flyers, too

Warmachines in KoW have mixed popularity. The common 5+ to hit is a major deterrent to most in their decision to include them. Taken in multiples however, they become a serious threat to flyers. At height 3 or 4 more often than not, your bolt throwers and cannons can target them rather easily. The high piercing numbers also deal with the 5+ and 6+ defense in this regard.

Dwarf Ironbelcher Cannon

A complex game

Kings of War however introduces us to more complexities as I mentioned above. History does not provide strategic direction on how to defend against a Drakon Rider Horde, a Terror, or a Coral Giant. Some units combine the traits of multiple battlefield roles being able to jump freely between them during the game. I find it's best to combat them with whatever battlefield role your opponent is trying to accomplish in that moment. The better general will find those match-ups and exploit them.

Spells and magic items are like throwing bricks into a wood chipper when it comes to standardizing a unit for a new player. These elements make a mess of complexities not at all captured within rock-paper-scissors counter measures. I consider this a balancing element to the game because it's not possible to take an army that can perfectly counter any one opponent. I've noticed competitive players trend toward value buys along with the best all-around performers. I still say playstyle goes a long way but mixing things up is likely to be the most critical element.

Diversifying your list means more $$$ for Mantic and other manufacturer's and more hobby time for you. Just be sure to hide the credit card statements from your spouse.

What counters do you employ?