Many people love to get a single kind of unit and just keep getting it. They will "mass" this unit throughout the game. This article explains the popular masses and how to deal with them (or concoct them yourself).
An Undead player will often mass necromancers (sometimes scattering some Abominations in) to raise skeletons. It is an easy mass to carry out. Just get two Temples of the Damned (A Slaughterhouse for Abominations) and you are set. You will also need to do all upgrades that effect skeletons as they will be your main army. Now, how to fend it off:
Humans
Priests are very good counter, using Dispel Magic to eliminate the skeletons. You can also build strong melee (Knights and upgraded Footmen) and fight it out. A Paladin is a good hero to have, as he can destroy the Necromancers from afar (Holy Light), and, at high levels, reincarnate his troops so they are not "skeletonized."
Orcs
A strong front of melee (Taurens) will do the trick. You can also get Wyverns and eliminate them from the air. A Far Seer with Chain Lightning is good against the Necromancers, and Whirlwind is also useful.
Night Elves
Night Elves should get Dryads for the same reason Humans should get Priests. Abolish Magic will eliminate most of the skeletons and the Dryads should have no problems dealing with the remaining Necromancers. When using Dryads, a Priestess of the Moon will greatly boost the damage of your Dryads, while Starfall will crush Necromancers and their skeletons alike.
Undead
Obviously you can counter mass, however, Abominations with a Dreadlord and Vampiric Aura is often successful. A Lich with Death and Decay is also good.
All races
Construct effective melee units, and purchase Wands of Negation, if available.
Massing Shamans is a good tactic, because of the spell Bloodlust. Two or three Spirit Lodges and you are ready to go. Make sure that you get a lot of them before you attack anyone. You may also want to get Taurens. An interesting combination is when you add Witch Doctors with Healing Wards. Now, how to stop this mass in its tracks:
Humans
Dispel magic can help shrink them down to size, though powerful melee is usually better. Mortar teams can be very helpful, though be careful to have melee protect them, or the Shamans will get too close for them to be effective.
Orcs
Counter massing is your best bet. Wyverns can also work, but they are very expensive.
Night Elves
The Dryad's Abolsih Magic can shrink the Shamans, just like the Priests', and Hippogryph Riders are also effective. A Priestess of the Moon is a good choice as Starfall can help thin out the enemy ranks.
Undead
A Necromancer mass is good. Frost Wyrms, though expensive, are also helpful.
All races
Construct air units units, and purchase Wands of Negation, if available. If playing multiplayer, attack them at the same time.
This is very similar to mass Necromancers. It usually consists of an Archmage with the Brilliance Aura and Sorcerers (maybe some Priests). Again, it is easy to concoct. Two to three Arcane Sanctus should do it. It is important that you upgrade the Sorceresses to the Master level, so that you can use Polymorph. Now, how to survive it:
Humans
Again, Priests are very good counter. Use Dispel Magic to return your Polymorphed units to there normal state. Melee units are again effective, and quick, agile units are useful as well.
Orcs
Orcs are the most vulnerable, as they don't really have a "Dispel Magic" spell. You can use Purge, but your units will be slowed. If you have a Tauren Chieftain, the Endurance Aura can help balance that. Your best bet is with strong melee or the Shaman mass.
Night Elves
Night Elves can use pretty much the same strategy as in the Necromancer mass: they should get Dryads for Abolish Magic a Priestess of the Moon to support them. Huntresses are good too, as they are cheap and can move quickly.
Undead
Use strong melee, primarily Abominations, and get Banshees. The Banshees can cast their Anti-Magic Shell on the Abominations to protect them from Polymorph. A Lich with Death and Decay is useful as well.
All races
Like the Necromancer Mass, construct effective melee units, and purchase Wands of Negation, if available.
This mass is very deadly. It can deal with almost anything, and is very powerful. You simply produce Hippogryphs with two Ancients of Wind and use Archers left over from the beginning of the game. Produce extra Archers as necessary. Also do the appropriate upgrades. Now, how to counter it:
Humans
Rifles and Gryphons are a good counter, and you can try Sorceresses as well. Be careful not be caught off guard, as it will kill you.
Orcs
Orcs can easily dispatch Hippogryphs with Wyverns and Troll Headhunters are good too. A Shaman mass is another good counter.
Night Elves
Night Elves can counter mass, or go Dryads and Priestess of the Moon. Druid of the Talon is another good unit to get.
Undead
Frost Wyrms are a good choice, though Crypt Fiends with Web are good as well.
All races
Air units and anti-air ground units are good. Towers are also effective.
These are some of the most popular Masses, not all of them. You can actually mass any unit, so I have covered the most frequently seen. The methods for countering them have not all been tried by me, but I have seen them used. Understand that whatever you do, don't hold me responsible if you fail. Good luck!
Mass Sorceresses are lead by an Archmage with the Brilliance Aura
It is necessary to have many Arcane Sanctums when massing Sorceresses
Priests are made to counter enemy Shamans
A mass of Shamans combined with Witch Doctors begins the attack
Necromancers raise skeletons from the slain enemies and allies to bolster their ranks