Mordheim
Mordheim is living proof that the better a game, the less GW will actively support it. It combines the good parts of playing Warhammer Fantasy (Interesting lore, cool models, variety) with none of the drawbacks (Overpowered magic, blatant stupidity), all wrapped up in a narrative skirmish game that kicks more ass than you could possibly imagine.
Setting
In the Warhammer universe, there was once a city known as Mordheim. Things were generally all right there, until a goddamn comet crashed into it, leaving shards of Wyrdstone around and generally destroying the city. This is bad for general business, but good for foolhardy adventures who really, really want to loot the living hell out of an abandoned city while killing other opportunistic looters. This is considered to be the default setting for Mordheim, although other books have built on this considerably, giving you options for playing in Lustria, the Border Kingdoms, and even far-off Cathay.
Continuity-wise, it's set about a hundred years before the current Warhammer timeline, which no one will care about when you're playing.
Warbands
Hoo boy. It'd be easier to say what Mordheim doesn't have, because there is a lot of extra material produced by GW, along with glorious fan-made material. But, to be complete, here's the list of 'official' warbands that are legal in your neighborhood GW store.
Mercenaries: Come in Avelander, Kislevite, Marienburg, Middenheim, Ostlander, and Reiklander varieties. Easiest starting warbands, by far; you're just different flavors of human with a few altered rules.
Beastmen Raiders: Whoo, Beastmen!
Carnival of Chaos: Glorious, glorious Nurgle-centric army. Generally do fairly well in the first few missions, but some of their rules (namely Nurgle's Rot) can and will completely screw over other players in a long-running game, by breaking their heroes into useless pieces of crap.
Cult of the Possessed: Chaos up in this shit! You start weak, then you get crazy strong, then hilarious mutation tables screw you over completely and you laugh because it's Mordheim, baby!
Dwarf Treasure Hunters: Slow, heavily-armored, and expensive, Dwarfs can be a force to be reckoned with. Just remember; you're a tough motherfucker, so keep your expensive heroes safe, and you'll rock out.
Orcs & Goblins Hordes: Greatest bringer of fun in Mordheim out there. Every turn, you need to roll Animosity for your warband; bad rolls can result in stupidity, in-fighting, or suicidally brave charges.
Sisters of Sigmar: Dead hard in the hands of a good player, Sisters get the coveted Steel Whip, one of the best goddamn weapons out there for players.
Skaven Warband: Initially, these guys get a bad rap. Then, you have fun playing with them. Then, you play a guy who runs a horde of naked Skaven carrying slings, and you hate everything forever, because it turns the game from 'hilarious, quirky skirmish' to 'being a beardy motherfucker'.
Undead: Generic undead list; nothin' too fancy here. Notable for the fact that most of their Henchmen cannot gain experience, so you really have a hard time when you lose a Hero in the game.
Witch Hunters: BURN THE WITCH! You get to shut down other magic users, plus their option to start the game by RELEASING THE HOUNDS is a fun and viable strategy.
At some point, someone needs to sit down and add all of the other warbands that aren't official, including those fucking Shadow Walkers.
Gameplay
At first glance, it's basically Warhammer Fantasy in a skirmish format. Then, you realize that it's goddamn awesome.
Each player starts the campaign with 500 crowns (or teeth, or slave tokens, or whatever the hell it is your race uses to pay the poor bastards who run around for them). You use this to hire Heroes and Henchmen. Each warband can hire a maximum of five (or six, if you're a fucking rat) heroes to start out; these are the most important characters in your warband, as they give you the much-needed Wyrdstone and gold needed to keep looting the city. You fill out the roster with Henchmen, who are somewhat less talented and inspiring than the rest of your heroes.
After hiring your models, you then buy equipment for them, and you're ready to start.
When a model loses its last wound, you roll a d6; they have a chance to survive and keep fighting after being knocked down or stunned. If a model is taken out of action, you roll on the giant table of injuries (for Heroes) to see if they've died, gained a crippling wound, or somehow picked up some awesome abilities due to scars.
As models survive games, they gain experience, which can give additional skills, stat increases, and power to your warband. This is the appeal of Mordheim; it's a campaign game, designed to let you create a characterful warband of unique figures.
There are a huge number of optional rules for Mordheim. It is generally suggested that you play with them, as they enhance the whole game experience to a huge degree.
Culture
If you read the above section, you can probably tell that Mordheim isn't the most balanced of games out there. It's not meant to be; if you're looking for a balanced, competitive skirmish game, you've come to exactly the wrong place. Random shit will happen (if you use that table), and you will laugh at it, because if Mordheim stands for anything, it stands for STUPID FUN.
Most games are played using a Gentleman's Pact, wherein the players agree on optional rules and what sort of strategies (Skaven slingwall, Shadow Walkers) are off-limits for the duration of the campaign. Narrativity is usually encouraged, as that's part of the experience.
Coreheim
An attempt to balance Mordheim; /tg/ alternately likes and loathes it, depending on the player. It removes a lot of the problems of Mordheim, while adding several new ones that are unique to Coreheim. It also completely misses the point of Mordheim; there's a limited selection of warbands (most of which are flavors of mercenary), the randomness is removed, and it tries to treat the game as a 'serious' wargame, rather than something that creates glorious stories to tell around the gaming table. They are also hilariously misogynistic, as seen in their explanation of why the Sisters of Sigmar were never added to their game.
It's a decent game, but it's not Mordheim.