It's my estimation that Starcraft is the distant, distant future of Warcraft. Azeroth is now Earth, most other races gone extinct except humans (now naming the planet Earth), and the Protoss are the now-demonic-free Eredar, possibly having merged their race with the Naa'ru. The Zerg was once known as the Scourge, no longer undead, but retaining many characteristics.

But this is just a guess and I also figure that Blizz will never have this explicit, and is more a series of subtle hints.

@ Mike

No, the origin of the Zerg and Protoss is quite explicitly stated in StarCraft and has no link to Warcraft.

The Protoss pre-date Eredar and Naaru anyway.

Honestly, I always saw it as all one Universe. With the Warcraft and Starcraft stories taking place in different galaxies or parts of the same galaxy but around the same time.

Odd, I don't see the resemblance past blueish-purple skin.
Protoss hand-to-hand weapons are almost literally their minds (the Psi-Blades) and their other weaponry is basic sci-fi fluff.

And Starcraft & Warcraft are, as said, separate fictional universes despite both games making nods to each other.

I do find it plausible that it's one universe with different galaxies, after all i didn't play SC1 but the 5 minute thingy said the protoss and zerg were created by the zel-naga (how do you spell that?) sound similar to the titans? also zergling is almost exactly like the fulhunter. could be some rogue fel hunters found their way into the zerg ranks or maybe some rogue zerglings were found by sargeras