Warhammer 40,000 is this trope to Warhammer Fantasy, though not by the margins of some other works on this page, as the source material was already parodying "Darker and Edgier" works by playing this trope to the extreme.
The first player's handbook removed the gnomes and replaced them with tieflings, who are no longer fiend-blooded mortals but the blood-cursed descendants of a Fallen Empire that turned to worship of Asmodeus in an effort to conquer the world and lost everything.
When gnomes returned in the second player's handbook, the previously wacky (if somewhat generic) gnomes had been given a new backstory as a race bullied and enslaved by the demented and depraved Fomorians, a race of deformed fey giants, which has left those free enclaves scarred and paranoid.
Half-orcs, meanwhile, were removed from the first player's handbook due to their Child by Rape backstory and were instead replaced with the Dragonborn, a Proud Warrior Race Guy species of Draconic Humanoids who used to rule an empire, but have been left as homeless wanderers ever since their empire was shattered in a war against the tieflings. When they returned in the second, half-orcs had essentially lost their rape-associations, being a true-breeding race in their own right whose pasts are mysterious, but mostly involve divine or arcane creation, or consensual Interspecies Romance.
Elves went from being super-perfect beings who were naturally gifted in both nature and magic to two races; the "masters of magic" became the Eladrin race, who are now a Fallen Empire that struggle ceaselessly against their Drow kindred and the above-mentioned Fomorians, whilst the Elves who retain the "ones who walk with nature" aspect are now those who were stranded in (or fled to) the mortal world, where they have lost the bulk of their magical nature from living outside of the Feywild.
The Aasimars, mortals bearing the blood of angels and celestial beings and the good counterparts to tieflings, were replaced with Devas; angels who either chose to forsake their immortal power and glory, or who were exiled to a semi-mortal existence.
Forgotten Realms definitely went darker, with glorious cathedrals crumbling and different gods and longtime power characters being slain or depowered left and right. Though one must remember that Forgotten Realms wasn't the only campaign setting, just the most popular; other settings, particularly Ravenloft and Dark Sun, were noticeably darker than FR was anyway — this more brought FR "down" to Greyhawk's level. Players still have Eberron, with its pulp-adventure-y feel, for less depressing fare.
On the third hand, the system is much Lighter and Softer, in that every adverse condition that happens to the players can be removed almost instantly. Several of the nastier conditions from earlier editions (e.g. attribute drain) simply don't exist anymore, and all of the others either automatically wear off in five minutes, or can be removed by a low-level spell. Hungry? Oh, here are some infinite rations. Room is dark? Plenty of infinite light sources around. The world may be dark and edgy, but harsh, long-lasting hardship for the player characters is non-existent.
But they do introduce quite a few nasty semi-permanent conditions in the 4e version of the Book of Vile Darkness. Which itself is actually a lot less darker and edgier than its 3e version and actually ends up a lot better for it.
The Pathfinder Adventure Paths and campaign setting have also gotten noticeably Darker and Edgier. The half-orcs' origins as the product are made more explicit, ogres are reimagined as inbred monsters right out of Deliverance, and most monsters explicitly like to eat people. Even the gnomes get in on the act. In Pathfinder, they are fey creatures who have been separated from their original world. If they do not constantly seek out new and ever more sensational experiences, their features begin to 'bleach', the banality of existence aging them to death.
The New World of Darkness actually plays with this. True, the world is, in general, more miserable and suspicious, but there aren't any looming apocalypses or sense that things are getting worse beyond the perspectives of individual people, and the moral fabric has been lightened a bit (even the Card-Carrying Villain groups have explicit Evil Virtues and actual reasons for what they do-however arcane those reasons are). Thus, it's only the prerogative of the Storyteller that decides if it's a World Half Full or not. And you know Lost? "World Half Full" is one of the basic premises of the game. You know what happens to the Lost if they avoid behavior they know is dangerous like maxing out Wyrd and not decreasing it after you start being hit with Clarity rolls? Absolutely nothing. This is in contrast to the old game, where it was either death or going Dauntain.
The 6th edition of Gamma World used the d20 Modern ruleset and was the grimmest, darkest edition of the game, period. While the first edition of Gamma World had been a parody of post-nuclear apocalypse, a Black Comedy rich game of wackiness, where one could see things like a laser rifle-toting yeti/cockroach hybrid, Gamma World D20 took everything seriously, making the backstory realistic (genetic engineering and nanotech vs. nuclear war) and portraying all of the horror inherent in such a ruined, freakish world. Gamma World 1e would point out the hilarious side of fighting a garbage grinding robot whose programming had gone mad: Gamma World 6e would emphatically point out what it would like to be on the wrong end of those grinding, snapping, mashing jaws and relentless, implacable hunger... For better or for worse, the 7th edition swung towards playing up the comedic aspect for all its worth.
Witch Girls was initially a lighthearted RPG parodying girls' shows like WITCH or Winx Club, but after the weird transformation fetishism inherent in the design was gradually revealed, it came out with a "Wicked Edition", supplements included primarily Nightmare Fuel monsters, a "Zombiegeddon" was scheduled focusing on necromancy-type witches, and the second edition is set to be titled "Book of Shadows".
Shadowrun, while already dark just simply doesn't let up with the 4th edition. One example is the Horizon Corporation, the only corporation without atrocities to their name has shown their true colors as they commit some rather heinous actions that features them. As of the 5th edition, they were shamed when they tried to control technomancers (one group they had been known to champion for the rights of) which ended in a brutal massacre.