The Keléstia
The Keléstia is a collective of seven linked parallel worlds in the family of Terra. The planets of Earth, Arda (Tolkien's Middle-earth), Narnia (C.S. Lewis), Kèthîra (Harn), Oerth, Uerth, and Toril. All seven are linked through Planescape. Not everything is exact, however under the high power, all the gods of Earth exist - the Norse gods, the Finnish gods, the Chinese and Indian gods, all sorts of pantheons who often bear the names of Earthly nations. Due to time distortions of language differences gods sometimes have differnt names, but many times can be traced to the gods of other planes. One could argue that this implies the Earth exists as their world of origin, or at least a world similar to “our” Earth in many respects.
Whether it's our Earth or merely a parallel one with similar nations, whether it still exists or whether it was destroyed long ago - these matters are dark to us.
Does “our” Earth exist in Dungeons & Dragons? Yes, it's appeared in a number of places. In “The City Beyond the Gate” in Dragon #100, characters from a D&D world must venture to London, England in 1983 to retrieve the Mace of Cuthbert from a museum. In The Immortal Storm, a party of godlike Immortals have to travel to New York and Chicago in pursuit of the essence of smell.
In Castle Greyhawk the PCs find a portal to Bombay, India circa 1945, and there's a whole sideplot where Mordenkainen travels to Hollywood (circa 1987) to make fantasy movies, casting the PCs in them.
It is was the common thought of originators Dungeons & Dragons that the elves of many of the worlds came from Tolkien's Middle-earth when they left Middle-Earth. The Forgotten Realms and Hollow world had migrations of people from Egypt, Mesopotamia, ancient Greece and Rome, and pagan Ireland in its history. These might well have been those actual nations from our Earth, though official materials leave this vague. Ed Greenwood wrote a series of articles in Dragon Magazine called “The Wizards Three,” which feature Elminster, Mordenkainen, and Dalamar (the elven wizard from Krynn) meeting together at Ed Greenwood's house (with Ed Greenwood hidden in a suit of armor, taking notes), swapping spells and sampling Earth cuisine. Occasionally other characters from Oerth or Toril have shown up as well. The conceit behind Ed Greenwood's Forgotten Realms articles has always been that these have been dictated to him by Elminster himself, who uses his spell Elminster's Worldwalk and various portals to appear on Earth and chat with him about the Forgotten Realms.
There is actually more than one Earth in D&D. In an ancient issue of Polyhedron, Gary Gygax spoke of the seven parallel worlds: Earth is the least magical and most technological of the five; Oerth is the most magical and least technological and Arda evolving away from magic to technology during an age of man. Murlynd, a quasi-deity who was originally a PC in Gygax's home campaign, has been to Earth; in the adventure Dungeonland the PCs explore his house, which is equipped with such Earthly conveniences as a VCR. In the adventure Castle Amber, the PCs go to medieval France, but not the France of our world; they go to the parallel Earth of Clark Ashton Smith, whose stories tie into Lovecraft's Mythos. In “Chronomancy and the Multiverse,” an article published on WotC's website (originally in TSR's AOL site), Roger E. Moore says that this Earth is the same as the Gothic Earth described in the Masque of the Red Death setting, and the same as the various fantasy Earth cultures described in the Historical Reference series of accessories: The Celts, The Glory of Rome, Age of Heroes, Vikings, A Mighty Fortress, Charlemagne's Paladins, The Crusades.
There's also Midgard, a Prime world entirely dominated by Norse myths, where the serpent Jormungandr literally wraps itself around the ocean, described in Dragon Magazine #90 and the 0D&D Northern Reaches Gazetteer.
The d20 Modern accessory Urban Arcana describes a version of Earth that has been secretly invaded by beings from the D&D worlds beyond the Plane of Shadow. One Planescape NPC exists there: the ogre mage Estavan, who's apparently found a portal from Earth to Sigil.
So yes, Earth exists in D&D, and even if it hasn't been explicitly mentioned in anything that says “Planescape” on the cover, I think you can say it exists in Planescape as well. The question is, which Earth do you mean? A portal from Sigil could touch many alternate versions of the world: an ancient Earth where the gods of Olympus still rule, a modern Earth where no one knows magic is real, and a modern Earth where elves, dwarves, (and orcs) have returned and are reintroducing magic to the masses, and a version of Earth where gods, vampires, and mages have always guided society in secret are just a few of the many possibilities.