Can the ghosts in Harry Potter interact with each other? I think I remember some games they played that indicated they were able to have physical contact. Is that right? Can they interact with each other on a physical level? Or would they just pass through each other?
http://harrypotter.wikia.com/wiki/Category:Headless_Hunt_games lists 4 games from the Headless Hunt in CoS:
Head Hockey Head Polo Horseback Head-Juggling Headless Bowling
While the first 3 have no details of them, sounds like to make the game work you HAVE to have inter-ghost contacts. As for Bowling, even mortals can play, presumably (it's 100% true in a computer game, but can only be inferred from a book):
Sir Patrick: "So, Harry me lad, care for a little headless bowling?"
Harry: "I'm not sure. What is it?"
Sir Patrick: "Just take your head off... not yours, we'll find one for you to borrow... roll it down the alley, and knock over the pins."
Ghosts likely are able to physically interact.
Ghosts likely can physically interact with each other, since they waltz at Nearly Headless Nick’s Deathday party.
“It was an incredible sight. The dungeon was full of hundreds of pearly-white, translucent people, mostly drifting around a crowded dance floor, waltzing to the dreadful, quavering sound of thirty musical saws, played by an orchestra on a black-draped platform.”
- Harry Potter and the Chamber of Secrets, Chapter 8 (The Deathday Party)
Waltzing typically requires a certain amount of physical contact, so presumably ghosts can indeed physically interact with each other.