EveryBig Bad who isn't a Disc One Final Boss decides that conquering the Digital World isn't enough - they also want the Real World as well.
Digimon Tamers: The D-Reaper attempted to delete Earth in accordance with its purpose once it was accidentally brought over into it.
The real king of this trope is Millenniumon who, as revealed intheWonderSwangames, eventually aspired to conquer all alternate-reality Digital Worlds (that is to say, effectively the alternate worlds of every Digimon canon ever). He comes dangerously close to succeeding, being particularly successful in being The Man Behind the Man as far as almost every bad thing in the Digimon Adventure canon is concerned.
Digimon Xros Wars: Baguramon is probably the closest in the franchise to rival Millenimumon in this aspect, and is probably second in power to Milleniumon as well.
The titular character of Noein who snapped after looking through countless universes to find one that didn't end in tragedy. After failing to do so he decided it would be better to tear down the multiverse and return everything to the void.
Infamous Countdown to Final Crisis gave us Monarch, who gathered an army of supervillains from the whole multiverse to fight its protectors, the Monitors. At the same time one of the Monitors, Solomon, plotted with Darkseid to conquer the multiverse. It's hard to say which one was worse.
Monarch was actually introduced much earlier in the (not very well-received) Crisis CrossoverArmageddon 2001, but he had nothing to do with the Multiverse (or the current Monarch, either).
In a Fantastic Four storyline, the Marquis of Death traveled through Alternate Earths, destroying them, killing everything, or any sort of villainy he felt like. All for fun.
Another Marvel villain, Abraxas, wants to conquer the whole multiverse, but is kept in check by Galactus - as long as Galactus lives, Abraxas can't even exist. Also yet another Marvel villain, the Beyonder. Marvel loves this trope too.
Exiles enemy Hyperion was a member of another team sent to repair alternate realities who killed everything in his world and become both a Dimension Lord and completely alone. However, instead of helping alternate realities he tried to conquer them.
The "Marvel Zombies Return" mini subverted that: the zombies are struck between two Earths - when they conquer one, they end up being sent to the second's past in an endless circle.
And then you have Hyperstorm, another Fantastic Four villain who's the future son of Franklin Richards and Rachel Summers. Let's drive this point home, shall we? Daddy can alter reality with his mind, and mommy is a cosmic-level telepath/telekinetic that can access the Phoenix Force. Obviously, their kid was tremendously powerful and conquered several universes in his adult life.
Another Marvel villain who semi-fits this trope is Kang The Conqueror, time-traveling military genius who's conquered universes, not through raw power, but through tactics and strategy.
Yet, another Marvel villain - Amatsu Mikaboshi, Chaos King, who is a void that existed before creation of the first Universe and The Multiverse and seeks to destroy it all, until nothing but him will remain.
And another Marvel villain, or rather bunch of those - the Many-Angeled Ones of the Cancerverse, beings that killed Death and conquered their Universe, and wanted to do the same to other Universes, starting with main Marvel Universe. Shuma Gorath is probably the most well known, and is the ruler of over a hundred universes.
Yulaw, from The One (2001). His ultimate goal is to kill all 124 alternate versions of himself from parallel universes to absorb their life force believing he'll become an invincible, god-like entity.
The rulers of Outworld from the 1995 Mortal Kombatmovie have to win 10 consecutive MK tournaments in order to conquer the realm of Earth. So far they've won 9.
Possibly H. P. Lovecraft's Mi-Go. In The Whisperer in Darkness it's mentioned that the ones present on Yuggoth are but a small outpost of an impossibly ancient and powerful civilization that originates from outside our universe. It's implied that they conquered their own universe and possibly others, and are now invading ours.
They don't seem that ambitious, at least on Earth, possibly because it's the reserved playground of Cthulhu et al. They're universally widespread, but don't seem interested in outright conquest unless it brings them extremely good payoff.
Appears in Skulduggery Pleasant as an unintended consequence of banishing the Faceless Ones. Although thousands of years ago they were thrown out of the main universe, it taught them the secret of dimensional travel, and for the past few millienia they have been jumping from universe to universe, devouring them entirely as they go...
In the Tramorea saga, this is what the Dark God actually a Sufficiently Advanced human Tubilok aims to do.
In the Magic Kingdom of Landover book, Witches' Brew, Rydall of Marnhull claims to be one of these, planning to make Landover his next conquest. Turns out he's actually a local nobleman, working with the titular witch to overthrow Ben.
Metatron and his angels in His Dark Materials. While they apparently do not want to rule physically, they do want to install their religious ideals everywhere. Considering the size of the angelic army in the final book compared to the sheer amount of universes with creatures in them to which the concept of "Religion" is propably very alien (the Mulefa), not to mention that several significant events (such as Jesus being born) may not even have happened in some of them, their prospects are propably not very good, although the books never bring that issue up. They get defeated nonetheless, by a - comparably - small opposing force consisting of locals of "only" a few universes and the final battle of the two armies, while fitted with grand and bombastic visual displays (such as the angelic cloud fortress) seems to be on a smaller scale than World War II and is certainly shorter - hardly worthy of a multiverse-deciding conflict.
The Champions verse had Tyrannon, an immensely powerful dimensional lord who seeks to conquer all dimensions. His being manifests in 888 bodies at once, of varying levels of power; his primary or "true" form, which resembles a gigantic tree and cannot move, lives at the heart of Thulkos, his native dimension. When he conquers one dimension completely, he merges it with his home dimension and forces its inhabitants to worship him and commit sacrifice. Doing so increases his power and his hunger.
The Fifth and Sixth editions of the setting added Istvatha V'han, Empress of a Billion Dimensions. She takes a more technological approach to dimensional conquest, as opposed to Tyrannon's mystic nature, and rather than merging dimensions, she consolidates her power through Bread and Circuses.
In Magic: The Gathering, there's Elesh Norn, the Grand Cenobite. She has seen that Mirrodin will merely be the first plane to fall to the new Phyrexia.
She inherited this from Yawgmoth, who built the old Phyrexia and set off to conquer every plane he didn't destroy. Fortheirown good.
The rulers of Outworld from Mortal Kombat must win an MK tournament within a realm in order to conquer it. They've won every single time and the realm of Earth is next.
The Guardian from Ultima Underworld II is capable of spanning multiple planes of reality at once and aims to conquer each one.
Dark Brain from Super Robot Wars game series travels through alternate universes and destroy them. Subversion, since Dark Brain doesn't care much about conquering the universes as seeking the 12 keys.
Count Bleck from Super Paper Mario. He's only going to conquer part of it, and then use the power gained from that portion to destroy the entire multiverse so he can not make a new one. Dimentio also counts.
Tyrant Overlord Baal from the Nippon Ichi-verse. Most high-level Overlords can and will conquer any netherworlds they'll get their hands on, but Baal is the most well-known, showing up as a Bonus Boss is almost all of the Nippon Ichi games.
Overlord Zenon from Disgaea 2 used to act this way in his youth, but seems to have settled down by the beginning of the game and is content with ruling only Veldime — or so everyone thinks up until it's revealed he's a fake and the real Overlord Zenon tries to go right back to destroying everything once released.
The Combine of Half-Life 2 and its episodes fit the bill as parallel-universe conquerors, having already taken over an unknown number of realities and adopting their lifeforms for use as highly-specialized weapons or slave labor, and stripping the realities of their resources until it's nothing more than a lethal rock. They're also capable of quick travel between these universes, but it's rather limited. The Xen and Race-X aliens (and arguably even humanity) of Half-Life may be parallel-universe warmongers on a smaller scale.
99, the Big Bad of Namco × Capcom. When player finally faces it, 99 is still missing half of its essence and instead use Saya for replacement. Yet it still has enough power to merge four dimensions together and resurrect groups of Big Bads to aid it upon its awakening. And this is just the beginning of its process to rule new - single - world.
YHVH is implied to be this in Shin Megami Tensei III: Nocturne. Untold billions of Earths rise and fall at his command only to rise again, all to create a perfect society that will never question his rule.
City of Heroes brings us the Rikti, who at first seem to be the classic Alien Invaders and are actually referred to as such throughout the First Rikti War. Turns out that they're actually mutated humans from a parallel Earth, who are going dimension-by-dimension and forcing the change one world at a time. It's implied that Primal Earth (the "main" world) was one of the first to successfully fight them off due to the presence of superheroes; they didn't fare much better on Praetorian Earth because about 95% of it is either blasted with nuclear fallout or overrun with the Devouring Earth.
It was recently revealed that Mechakara was attempting this as well.
Ano now, as seen at page quote, Lord Vyce. It's revealed by none other than Vyce himself that he only does this to protect the multiverse from something worse. And he takes out Pyramid Head with a single stab from his weapon, in between beating Linkara senseless with his bare hands.
Vyce may be a subversion: In a later episode, Linkara says that he did some checking and discovered that Vyce would only conquer a couple of planets before moving on to the next parallel world. Vyce makes the point that conquering an universe would cost a lot of time and resources that he didn't have, but Linkara still uses it to mock him for not being as awesome as he claims to be.
Vyce also shares a history with 'The Smiling Man' mentioned above, since the villain appeared in the 'Lightbringer' webcomic which was also created by Lewis Lovehaug. As well as A similiar punishment upon defeat. Since both are stranded on a world in another reality with no intelligent life and only basic supplies for survival.
Towards the end of Spider-Man: The Animated Series, a different universe Carnage-Spiderman goes psycho (more than usually Carnage goes) and tries to destroy all the Universes. It's up to a group of alternate-Peter-Parkers to stop him.
In Transformers, Unicron is a Planet Eater who wants to eat everything. One planet at a time, one timeline at a time, one universal stream of branching timelines at a time, in sequence. When he says he wants to be completely alone, he damn well isn't beating around the bush. Even if he's destroyed in any one universe, he just gets shunted to another to start over again thanks to mucking about with different flows of time across the multiverse. Oh, sure, there are a few permanent methods of dealing with him, like trapping him in a physical form to slow him down, but if they go horribly wrong, well...
One Comic has another Multiversal constant state that he has so far consumed some 47% of the known Multiverse. Yeah. Not mucking about.