Pretty self explanatory, but every major event seems to have a red carpet. Is this the case worldwide, or is it an American/Western/etc. convention? When did this become the symbol that an event was something worth paying attention to?
There is a mention of a "crimson path" being laid out for use by the title character in Aeschylus's play Agamemnon, but the circumstances and symbolism are sufficiently different from the modern-day norms that I'm inclined to dismiss it as a coincidence.
Aneccdotately, the practice laying down a special ground cover such an an exotic oriental rug, along the processional path of important persons, is well documented in paintings and literature from the Middle Ages onward, in both Europe and Asia. However, I've been unable to find a trustworthy citation for this factoid, so I think we should treat it with suitable skepticism.
Current research by the Smithsonian suggests that the modern ritual of specifically using a long roll of red carpeting or other textile as part of the public processionals of important personages, dates back no earlier than 1821, when President James Monroe was provided with a plush crimson carpet when he ceremonially disembarked from a riverboat when on a official visit to Georgetown, South Carolina. However, even this date should be treaty with suspicion -- despite being widely repeated, I've never seen a primary document that mentions a red carpet as part of James Monroe's 1821 visit to Prospect Hill in Georgetown, SC.
More realistically, the current use of a red carpet only dates back to the late 19th or early 20th century, when it was used by railroads as part of the boarding procedures for their first-class or VIP-only carriages. This use by the New York Central Railroads' "20th Century Limited", which traversed the route from the New York City to Chicago, is well-attested in many contemporary sources including this advertising pamphlet from 1921, which describes the practice as already being well-established even then. The above-mentioned smithsonian article then goes on the describe how the use of a red carpet for the ceremonial procession of a (supposedly) important person was already part of the common idiom by the 1930s, and had been appropriated by Hollywood by the time the Academy Awards were first broadcast in color in 1966.