When it comes to the D&D universe, how many crossovers exist changes based on edition. Once it was considered canon that both Greyhawk and the Forgotten Realms existed together and travel between was possible. These days it's not explicitly stated one way or the other. Just as it was once considered that Earth was an alternate universe to Oerth and reachable by magic.
Generally speaking, you have your Prime Material Plane(Oerth, Faerun, Krynn, whatever)and the cosmology of other planes(Inner, Outer, Transitive)surrounding it. The setting for the Neverwinter MMO, as well as the Neverwinter Nights, Baldur's Gate and Icewind Dale games is Faerun, the Forgotten Realms, created by Ed Greenwood and home to fictional characters like Elminster and Drizzt Do'Urden.
Oerth is the home of the Greyhawk setting, where characters like Mordenkainen and Robilar are found. Krynn of course is home to the Dragonlance setting and its various characters like Raistlin Majere and Tasselhoff Burrfoot. Other worlds include Athas(home of the Dark Sun setting)and Mystara(aka the Known World, the basic D&D game setting). Other settings put the focus out on the planar cosmology(Planescape)or specific demiplanes(like Ravenloft, set upon the so-called Demiplane of Dread).