Wood

I can have many shapes and sizes

Wood comes in many forms of trees

I can have many styles and alter people's mood

You can make an statue out of wood. Depending on the statue someone's mood may change if it reminds them of something in the past.

I am used in a famous game

Chessboards are commonly made out of wood

I am used in many movies

Many movies have wooden cabins, with wooden furniture. Forests that have plenty wood, etc

  Some objects can be made of me

  Chessboards, doors, furniture, etc Of course, this opens the possibility of of other materials aswell, like stone for example.

Wood

I can have many shapes and sizes

Wood comes in many forms of trees

I can have many styles and alter people's mood

You can make an statue out of wood. Depending on the statue someone's mood may change if it reminds them of something in the past.

I am used in a famous game

Chessboards are commonly made out of wood

I am used in many movies

Forests that have plenty wood, etc. Some objects can be made of me: Chessboards, doors, furniture, etc

Of course, this opens the possibility of of other materials aswell, like stone for example. But I don't know