MetroidVania

1. Being a platform game (some people say a game hitting all the other criteria but not this one can't be a MetroidVania)
   
2. Having the freedom to explore in different directions, and the ability to progress in multiple areas (nonlinearity)
   
3. Having the whole game take place across one vast map/level
   
4. Acquiring new abilities/items/spells etc in one place that allow you to reach new areas in a different part of the map (just keys don't really count)
   

• The Metroid series before the Metroid Prime games which are first person shooters
  
• The Castlevania series after the Super Nintendo games which miss criteria two, three and four
  

• Exile (the SuperiorSoftware one, that is)
  
• FreeGames/AnUntitledStory
  
• [Robot Wants Kitty] (only 15 minutes long, but it does hit the criteria with the possible exception of "vast") and the rest of its [series]
  
• [Pieces]
  
• La Mulana
  
• Aztaka
  

• Aquaria (semi-avoids #1, as it's mostly not quite a platform game)
  
• Iji (has 10 levels accessed linearly, but within each large sprawling level definitely counts)
  
• The reason for the PlatformGame? criterion appears when you start considering things like LegendOfZelda, which in some of its incarnations would meet the rest of these criteria, but doesn't "feel" like what a MetroidVania should "feel" like.
  
• [CaveStory] is rather more linear than many such games, but enough of a classic (regardless of whether you like it) that it should be mentioned.