"Wizards can leave an imprint of themselves upon the earth, to walk palely where their living selves once trod, but very few wizards choose that path."
-- Nearly Headless Nick (OP38)
There are at least twenty ghosts that reside at Hogwarts (PS7). Each of the four houses has their own house ghost; Nearly-Headless Nick is Gryffindor’s ghost, the Bloody Baron is Slytherin’s, the Fat Friar is Hufflepuff’s and the Grey Lady is Ravenclaw’s. When ghost-related decisions must be made, they hold a “ghost’s council” (GF12).
JKR says Hogwarts is the “most heavily haunted dwelling place in Britain” (PM). Some ghosts come to Hogwarts after they die, for example the Grey Lady and the Bloody Baron. In contrast, Moaning Myrtle was murdered at Hogwarts, but left to haunt Olive Hornby until the Ministry ordered her to stop and she returned to the place of her death (GF25).
The ghosts are pearly white and glow (PA9).
Ghosts communicate with each other by ghostly letters. Nearly Headless Nick received one from Sir Patrick of the Headless Hunt. He must have used something of that sort to invite people to his deathday party, too (CS8).
Only witches and wizards can become ghosts (OP38)
Ghosts can communicate more effectively with people than the portraits. [Read the exact quote from Edinburgh Book Festival, 2004]
Ghosts were people who were very afraid of death. [Read the exact quote from Edinburgh Book Festival, 2004]
If a teacher is head of a Hogwarts house, we can assume they were in that house; that goes for ghosts as well. [Read the exact quote from Jo's website]