Mook Medic

Well, it's a battle like any other. You were walking about in the game and your enemies decide to drop in, just like they usually do. Huh, that enemy looks different. But that other guy has an area attack, so you'd better take him out first. *bang bang bash maul mutilate* OK, it looks like he's almost gone, time to finish him off... Wait a minute- is that new enemy healing the enemy you just worked so hard to destroy? That's cheating!

This trope refers to Mooks that heal other Mooks. Sometimes these guys can revive dead Mooks or take them from the brink of death back to full health. Other times, all they can do is delay the inevitable. Either way, it is usually a priority to defeat these enemies first.

Examples of Mook Medic include:

Tiberium Sun has the Medic. Left to their own devices, they'll extend the life of any infantry based enemy considerably.
Golden Sun has several enemies, including the Phoenix, which are capable of resurrecting their defeated allies.
The scarab in Sacrifice, which automatically shoots healing energy at any injured ally within range.
Doom II: the Arch Vile can resurrect almost all slain monsters.
Several maps in Fire Emblem have Magic-users with long-range healing staves.
The Cleric Grablins in Costume Quest.
Several in the Dragon Quest series - mostly Slimes. They tend to have very obvious names, such as Healslime, Cureslime, Sootheslime and King Cureslime. Anytime they appear grouped with other enemies, you'd do well to take them out first. Conversely, in the Dragon Quest Monsters series, where you use classic Dragon Quest monsters as Mons, having one of those in your party at all time is a good idea for most of the game's duration.
Diablo has a few of these: Zakarum Priests, Council Members and Overlords, and Unravellers counted as well.
Some pets and minions in World of Warcraft.
- Kurzan Medicine Men can be a nasty surprise to a new player first entering Stranglethorn Vale. They tend to pair up and heal each other. They can be unkillable if you cannot kill or incapacitate one of them right away.
The Shining Force series also has this, preferably with the words "dark" and "evil" to describe the healers. The second game (as well as the Sega CD version of the two Gaiden games) make it more clear by having an evil bat-wing fairy show up whenever a healing spell is cast.
The Kingdom Hearts series have certain Heartless that heal their allies. Some examples are the "Green Requiem", (which float around and are resistant to magic), and the Crescendo (which can also summon other Heartless, at least in certain games).
There's a fun example in Breath of Fire III, with the the ZombieDr. He casts powerful all-targeting healing on his party, unfortunately they're all zombies too.
Wizards in Castlevania: Curse of Darkness; it's usually a good idea to get rid of them first.
In the flash game Captain Dan Vs. Zombie Plan, there are zombie medics.
Similarly, the Engineers in Halo: Reach give all the Covenant in the area overshields.
Guild Wars: enemies in the game use the same classes that players do, including healing specced enemies who fill this role.
Shaman Goblins in Torchlight.
In RuneScape, Tztok-Jad summons healers halfway through his fight.
In City of Heroes, there were the Tsoo "Sorcerer" minions. These little bastards not only healed their fellow mooks, they also teleported out of range when they weren't healing your enemies, so that you were forced to either track them down (and get slaughtered by their mainstream mook allies) or just focus on their allies, and wait for them to come back and heal them, making it all futile. Oh, and they were just as likely to teleport ahead where there were more mooks as back into the area you cleared, so tracking them down could draw more fire. Not too bad if you had some sort of immobilization or hold, but if you were a standard melee class, you were pretty much screwed.
- Just as annoying were the Immune Surgeons of the Cimerora zone, even though they didn't teleport. Fortunately they didn't appear anywhere but that zone.
- The Ghouls found in the Praetorian Underground are even more annoying -- they aren't medics normally, but whenever one is killed he emits radiation that heals any other ghouls nearby. It's possible, when used on ghouls, for even the most damaging AOE attacks to result in only a couple deaths -- and every other enemy in the target zone healthier than they were before.
Champions Online has "atomic reanimators" in the desert zone who not only blast you with radiation, but can raise mutants you've just slain back from the dead and send them rampaging towards you. And unless you're ramped up to the point you can one-shot them, they WILL reanimate something before they bite the floor....
The Borderlands "The Secret Armoury Of General Knoxx" DLC introduces Crimsom Lance Combat Medics, who can plant towers which heal nearby Crimson Lance units (similar to Roland's sentry will with the right upgrades).
White Magikoopas and Medi Guys in Paper Mario.
Glowing Ones from Fallout 3 can emit radiation that simultaneously injures the player and heals other feral ghouls.
Final Fantasy Tactics had a level consisting of facing five of these. It's not that hard, but it gets to be That One Level just out of sheer annoyance.
In Sonic Heroes, there is a robot who randomly heals all mooks onscreen (including himself) at once. If flipped over, he'll turn into a Bandit Mook and steal your rings.
The Power Robots in EarthBound can "replenish a fuel supply", which completely restores their own or other enemies' life.
Enemy mages can often heal other mooks in Dragon Age Origins. This is one of many reasons they're a top-priority target for a party that wants to stay alive.
Some powerful geth in Mass Effect have repair drones that hang around near them. Fortunately the repair drones are both uncommon and easy to kill.
Priests in Master of Magic can throw Healing spell once per battle. Both Priests and weaker Shamans have "Healer" ability that speeds up hit point recovery per turn for all units (except Death Realm related and Undead) in their stack, plus weak melee and magical ranged attack.
Age of Wonders has Priests (and Shamans for some races in the first game) with Healing spell and some or other magical attack.