Is Herobrine real in Minecraft?

Herobrine never existed.
It was a hoax by a popular multiplayer server that went viral on Youtube. The server claimed that Herobrine was the representation of Notch's dead brother.

This deeply infuriated Notch, who threatened to block the accounts of those responsible for the rumours, because Notch does not have a brother, dead or alive. The videos were removed from Youtube following Notch's warning and a Twitter post went up from Notch dismissing the rumours of a dead brother and denying that Herobrine exists.

You'll see "removed Herobrine" from the changelogs in recent updates. This is basically Notch and Jebs way of trying to get people to shut up about the fictional and unwelcome hoax-created character.