One thing that stood out immediately is the old-timey cartoon aspect of the visual design. Cuphead looks very similar to an old Mickey Mouse cartoon. Other critics have added Popeye and Betty Boop to the list of inspirable sources.
Some have said that Cuphead was inspired in part by the Mickey Mouse game, World of Illusion, which came out for the Sega Genesis in 1992. While it certainly is evident that Cuphead resembles Mickey Mouse, the games are very much different art styles. Cuphead is way more old-school, and World of Illusion does have decent graphics given the console, but World of Illusion is cast more in the actual Disney universe, whereas Cuphead has the freedoms and fresh animations of an indie title. Both games feature platform elements and co-op gameplay, but a clear line of inspiration is thin at best. Cuphead is a revolutionary addition to the platforming genre.