Quick answer: no. Your games are not considered by the courts to be your property. Games are not copyrightable. Annotations are, since they fall under the creative realm of writing. But the game pre-exists the players (they didn't create the game of chess--unlike Monopoly or Scrabble) and the playing of it can produce the same outcome again & again if people just happen to make the same moves.
A chess puzzle, as a composition, is (I believe) copyrightable.
When I play a game of chess I am in fact creating something (not sure what) along with my opponent. The result of that creation is a game notation stating the moves of the game played. If I also then create a chess puzzle then that will also have a game notation which is its solution. Both these would be in the first instance my creation along with my opponent (provided it isn't a chess programme, e.g. Fritz, Rybka) and in the second instance, the creation of a chess puzzle, which would be my sole intellectual creation (property).
So I what I want to know is are these creations my sole intellectual property? My copyright? To do with as I see fit and for no other person to use without my permission?
Now from my point of view I can see from the PGN's that I can download from other people's games that this isn't the case, but I don't know why it isn't.
Also I need to clarify that as someone who needs to keep inproving in chess I think it's essential that our games and puzzles are freely shared because in this way we are helped by the experience of others.
Hope there are some legal eagles out there who could clarify this for me.