There are a few reasons why your rating may not change at the end of a game:
If You Are Playing An Unrated Game
Your rating won't be affected if you are playing an unrated game. Check the 'Details' tab next to the game board to see if it was a rated or unrated game. During a rated game, you can also use this tab to see a preview of the ratings changes. Just click where it says 'show rating adjustment.'
Aborted Games
If a game is Aborted it will have no effect on ratings. Aborted games also will not show up in game history or archives, it will be as if the game never started! You can read more about aborting games here.
If You are Playing the Computer
Computer games are never rated, so if you are playing against any of our bot personalities or the engine, this will never affect your rating.
Daily Games
In Daily chess, the game is not considered to have 'started' until 4 moves, so if a game ends before the 4th move either by timeout or resignation, there will be no rating change. Checkmates in less than 4 moves will cause rating change!
Daily Games Exception
Please note, if you resign from a tournament in progress, even with no moves played, it will still affect your rating!