Mordhiem (and the similar, sci-fi Necromunda) seem to retain a cult following long after they "died" and though GW is returning to a smaller-scale focus with Age of Sigmar, it is apparent they are more interested in a Warmachine-style game rather than a true skirmish game.
A lot of rules have tried to recapture that feeling (and the playerbase) and failed.
Here are a few that immediately come to mind....
LOTR: SBG (and spin-offs)
This was a remarkably clean ruleset with some subtle mechanics. Perhaps a bit too subtle for the usual GW crowd. The Battle Companies campaign rules offered a simpler Mordheim alternative for adventuring in Middle Earth. To be frank, the dark ages LoTR world is a bit too bland to make people excited about it. It doesn't have the pizzazz of chaos demons, lizardmen, and rat-people. Ironically, the original orcs-elves-dwarves-goblins suffers from the popularity of its creations. It's just a little dull. I mean, the most powerful magic artifact simply turns you into an invisible drug addict?
Battle Companies was likewise a bit too simple/bland. Whilst sensible and clean, I don't think it has enough bling to allow you to pimp your warband.
Song of Blades & Heroes
For a while, this was the default response to "what fantasy skirmish game should I get." An awesome "build your own warband" toolkit allowed you to use any random model in your collection, and a clever activation system initially obscured its faults. Using only 2(!) stats necessitated adding 100s of special rules to add "detail." Quick, creative fun if you have like-minded friends, but more home-brew rules than club ruleset. Having to buy 3-4 pdfs for the complete rules means you have to pay $40+ for a bunch of pdfs - I'd expect a hardback rulebook for that price. Fun for a while, but ultimately lacks depth.
Some clever ideas but somewhat obtuse and overcomplicated rules. Had awesome, awesome metal minis years ahead of their time; but an ill-advised switch to prepainted plastics killed the skirmish game and the company.
Empire of the Dead
Basically a steampunk LOTR:SBG with its serial numbers filed off, and d6s replaced with d10s. Rode the initial wave of steampunk enthusiasm a few years back. Does seem to have a steady following, but it's not really tearing up any trees. Most LOTR:SBG comments apply. I suspect most play it for the quirky steampunk vibe and the fun models that come with it, rather than scintillating gameplay.
Infinity the Game
Quite possibly the best skirmish game out there, of any genre. However, it does not have a progression system, the chaotic characterful "levelling" and equipping your character that Mordhiem/Necromunda had. They had their chance with Paradiso campaign book, but it was a big letdown. They seemed to prefer strict "balance" and rigid mission structure instead. I think they're missing the point of a narrative campaign. Also, with each release Infinity is increasingly bogged down with extra rules and abilities until it is some sort of overcomplicated behemoth with more errata than the most involved RPG. It's ironic to say, but Infinity has been so supported and successful it's bloated from being a great game to merely good.
Probably the closest Mordhiem analogue. A fairly bare bones game at its core, driven by a thorough magic system. Definitely a "casual" game as its campaign system as it stands is a bit (very?) open to abuse by powergamers. I'm not a huge fan of hitpoints for individual infantry, though. And I was kinda hoping for a character creation system, although the generic templates do cover most things. A nice shiny book for a bargain price - no reason not to check it out. Dig out those old fantasy minis!
Hmmm. Did I miss any key players?
Anyway, despite the fact I've played all the above (OK, Confrontation only against myself a few times in a vain attempt to decipher the rules - minis are awesome though) and whilst Infinity and LOTR are some of my favourite games, I don't think the skirmish-campaign-gaming thing has been nailed yet. At least for me, all the contenders are a bit lacking. It's a topic I plan to explore over the next few weeks, given I have a lot of Warmachine/Hordes fantasy models coming off the painting presses and I have no real interest in the official rules. Maybe it's time to dust off my homebrew "Middlehiem" rules...