Melee in 5v5 was popularized by Serennia in his Warrior / Rogue / Enh. Shaman and 2-healer set-up which he tried to dub 'Trifecta'. Trifecta never stuck, of course, so Cleave became a more popular term coming both from the Warrior ability and the fact that a target descended upon by multiple melee will feel like she's being cleaved in half. More than a few clothies have cried foul, and some have accused such comps as being brainless, skill-less, and -- pardon me quoting the term -- "gay". [EDIT: No, it is not okay to use the term "gay" in a derogatory manner, let's just make that clear.]
The accusation comes from the fact that the idea behind a Cleave team is very simple: pick a target and kill it. The idea is to apply constant pressure on the opponent. Because Cleave teams have extremely limited crowd control options, the only recourse is to apply so much pressure on one target that it almost acts as CC. A Warrior or a Rogue (or both) is required to make Cleave work because of the all-important healing debuff inflicted by Mortal Strike or Wound Poison, making their target difficult to heal through. Cleave trains also need to take the initiative because Warriors need to get that Charge off and Rogues need to Sap and get the opener. It's fast, it's simple, and it's effective.
In 3v3, Cleave compositions consist of two melee and one healer. Warrior / Rogue / Druid is a popular comp solidly above the the 2000 and 2200 bracket. In fact, one set-up that sees the underrepresented Shamans and Paladins doing well is a Cleave comp of Warrior / Ret. Paladin / Resto. Shaman, which has good representation above the 2000 bracket. In 5v5, seeing a Warrior and a Rogue together is extremely uncommon because the two serve similar functions and have similar abilites -- Kick and Pummel, Crippling Poison and Hamstring, and Wound Poison and Mortal Strike. On the other hand, if you're leaning towards a Cleave comp, applying all those on a single target (even if they don't stack) isn't a bad idea at all.
The point is, Cleave teams work with blinders. They tunnel vision one target and pound it into submission. This is both the comp's strength and weakness. A Druid healer in a 3v3 Cleave comp, for example, will focus on throwing offensive Cyclones to keep the opposing team's healer out of play long enough for her teammates to kill a member of the opposing team -- more often than not a clothie. A Shaman healer will spam Purge on the kill target to remove as many defenses and Heal-over-Time buffs. The occasional Priest healer has Dispel Magic and Mass Dispel. A Paladin healer would... well... do nothing. There's a reason Paladin Gladiators have dropped in number over the past three seasons, you know.
Sometimes, Cleave teams would swap targets in the event of an immunity effect such as Divine Shield or Blessing of Protection. Other times, they rely on the quickness of their Priest or Shaman to dispel such immunities. Again, the idea is to keep a strict focus on one target until it succumbs. Done correctly, it is virtually impossible to heal through multiple melee attacks with a 50% healing debuff applied. Once Blessing of Protection and / or Pain Suppression is gone, you're pretty much guaranteed a dead target. A Cleave team's favorite targets are Shadow Priests and Warlocks, even those specced with Soul Link. With no natural kiting ability or improved mobility, Warlocks explode when they come into contact with Cleave teams.
Actually, most clothies explode with Cleave and that's the beauty of it. A clothie with multiple melee beating down on her will not be casting anything that's not instant. Not easily, anyway. This is largely why players feel that Cleave teams are "ez-mode". There's not much thinking involved. There are few intricacies that lie between picking a target and zerging it until it dies. Everything, and I mean everything that the Cleave team does must be focused towards bringing that one target down. Disrupt that focus and you've taken the first step towards beating Cleave.
So how do you deal with Cleave teams? Simple. Outlast them. A Cleave team isn't built for longevity. With limited CC options such as Intimidating Shout and Blind, Cleave teams are ill-equipped to control a match. The only real control comes from the pressure they can apply to a target. Ease up on that pressure and you've already gained an advantage. Snaring, freezing, or crowd controlling one or two of their DPS reduces their pressure considerably. Applying converse pressure on their healer works, too. If a Cleave team doesn't drop an opponent within the first thirty seconds of a match, their chances of winning begin to slim down because they start to run out of natural methods of escaping a kite.
A Warrior in Entangling Roots will escape once through trinket. The rest of the time, she'll be yelling over vent for her support to dispel it or give her Blessing of Freedom. Even a Rogue can only Shadowstep every thirty seconds and Vanish every five minutes. The idea is to break the zerg, trying to keep the Cleave target alive through all means possible and applying pressure on the other end. This is why triple healer teams in 5v5 are painful match-ups for Cleave. At a certain point, the melee opponents will be supremely kiteable through a well-laid Frost Trap or unnoticed Earthbind Totem.
Easier said than done, of course, but the comp with the simplest strategies often also have the simplest solution. This is why Mages have a decent chance against Cleave, because the combination of Frost Armor, Blink, and Frost Nova are bad news for them. Ice Block even buys the Mage some time. The goal is to kite, heal, and control throughout the match. Accomplish this long enough and even the all-powerful Cleave train will run out of steam.