Over the years, I've tweaked my neck a few times lifting: once during bench press, once during OH press, once during KB swings. The pain usually originates in my upper traps and travels all the way up the neck, making it very stiff. Usually it's a very mild injury that causes minor discomfort, but once it was bad enough that I couldn't turn my head, which made crossing streets, driving and even lying down quite painful. However, every time it was the result of poor technique: lifting my head and oddly squirming on the bench, improper head position on the OH press, and yanking my head back during heavy KB swings. Moral of the story: make sure you learn and maintain proper head position for all your lifts and aren't straining your neck in weird ways to complete a rep.