I was just asked to clarify whether the words "jack" and "gank" mean exactly the same thing or whether they have subtleties that set them apart.
I'm happy to oblige.
And for fun, I'm going to throw in another related word: bogart.
"Jack" generally implies that whatever is being taken is of some value, was taken without permission, and is not going to be returned. "Someone jacked my hat while I was at lunch." Jacking may also occur with permission though, but definitely connotes that it's not going to be returned. "Can I jack a couple sheets of paper?"
"Bogart" refers to something that has little value, or is meant to be shared, disposed of, whatnot. It's most often with permission. It may also refer to something that's going to be returned. "Can I bogart your pen for a second?" or "Mind if I bogart a stick of gum?" It might be done more stealthily though, as in, "Someone's been bogarting paperclips out of my cup; I hardly have any left." Bogarting can also mean to hog something or take more than one's share; this use is especially common among potheads: "Quit bogarting the stash."
"Gank" is also a form of harmless, minimally annoying misappropriation of goods, though it has the definite implication that there is either more of the good still left ("I never buy ketchup; I just gank a ton of packets when I'm at Burger King.") or that something is being ripped off, but without actually removing it from the original source, as in, "Oh, I just ganked the text off of the hotel website and pasted it onto the conference flyers."