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The term "Metroidvania" refers to a whole sub-genre of 2D action-adventure platform video games involving non-linear exploration and gaining new abilities to access otherwise closed off areas. The name is a combination of the series names "Metroid" and "Castlevania", both of which popularized the genre. Metroid games have always been non-linear with progression made by accumulating new powers, while the Castlevania series started off as a straight platform adventure series. Drawing on the Metroid games and Castlevania II: Simon's Quest, Konami created Castlevania: Symphony of the Night for the PlayStation. Ever since, the Castlevania series has also been known for its non-linear gameplay as well as its trademark action RPG elements. There have been many other Metroidvania games, however; some are lesser known and some feature popular characters like Kirby and Spider-Man.
The following is a list of games that fit the Metroidvania criteria. If anyone out there knows of any more, feel free to leave a comment). =]