The noble gas used in glowing advertising signs that produce a bright red-orange light is neon.
Neon is a colorless, chemically inert gas under ordinary conditions, but it glows a distinctive reddish orange when an electric current passes through it at low pressure. In a sign, the gas is sealed inside a shaped glass tube; the electrical discharge excites neon atoms, and the atoms emit light as they return to lower-energy states.
British chemists William Ramsay and Morris Travers discovered neon in 1898 while separating gases from liquefied air. The name comes from the Greek word neos, meaning “new.” Georges Claude demonstrated modern neon lighting in Paris in 1910, and neon quickly became associated with commercial advertising.
Not every colorful tube called a neon sign contains neon. Different gases produce different colors: argon commonly gives a lavender or blue glow, while coatings and fluorescent materials can create additional shades. Krypton and xenon are also noble gases, but they are not the canonical answer for the classic bright red-orange glow described in this question.