Nowadays, almost every bigger city hosts a film festival. Some focus on special interest contentwise (e.g. horror, sci-fi, LGBT) while others focus on the type of film: Animation, documentary or short films. There is a film festival for almost everything and everyone. Here is a list of the most important and traditional festivals. Do you know which cities are famous for their film festival? Countries and year of first festival given.
Selection of festivals is subjective - however, only festivals that exist for at least 40 years are considered (which excludes e.g. Tribeca, Austin and Sarajevo)
Many of the selected film festivals show short films, but the ones mentioned under "International Short Film Festivals" specialize on it