A term used to mean "Mess With" as in "I'm going to dink with that until it works". Along similar lines, in computer science, to increment or decrement a counter. "In counting from 4 to 6, it dinks the counter two times".
An onomatopoeia for the sound when a golf ball goes in the hole.
Military slang for a recruit in training, "Desperately In Need of Knowledge"
In Counter Strike and Counter Strike: Source, a dink refers to taking damage from a headshot but not dying. It is called a dink because of the sound it makes when the player is shot in the head with a helmet (It makes a sound similar to saying "Dink").