That looking too closely at the screen will blind you or damage your eyes. This myth originated decades ago in the 1960s from an advertisement by a television manufacturer. Basically in 1967 General Electric reported that their color TVs were emitting too many x-rays due to a factory error, so health officials recommended keeping children and pretty much anyone else at a safe distance from the screen. The problem was soon resolved, but the myth endured.

If you ask me I would say that x-ray radiation has little to do with going blind, I have no idea if radiation can actually make you blind, but it's funny how somehow eye diseases got in the way as the only possible consequences in the myth just because we use our eyes to watch TV.