Updated, 2019:
Since this question was asked there was a change to npm, such that --save has become the default option, so you do not need to use --save to update the dependencies.
Original Answer:
npm install <package_name> --save installs the package and updates the dependencies in your package.json.
npm install <package_name> --no-save installs the package but does not update the dependencies as listed in your package.json.
npm install <package_name> ---save-dev updates the devDependencies in your package. These are only used for local testing and development.
You can read more at https://docs.npmjs.com/getting-started/using-a-package.json.