How can I update NodeJS and NPM to their latest versions?

Use:

npm update -g npm

See the docs for the update command:

npm update [-g] [<pkg>...]

This command will update all the packages listed to the latest version (specified by the tag config), respecting semver.

Additionally, see the documentation on Node.js and NPM installation and Upgrading NPM.

The following original answer is from the old FAQ that no longer exists, but should work for Linux and Mac:

How do I update npm?

npm install -g npm

Please note that this command will remove your current version of npm. Make sure to use sudo npm install -g npm if on a Mac.

You can also update all outdated local packages by doing npm update without any arguments, or global packages by doing npm update -g.

Occasionally, the version of npm will progress such that the current version cannot be properly installed with the version that you have installed already. (Consider, if there is ever a bug in the update command.) In those cases, you can do this:

curl https://www.npmjs.com/install.sh | sh

To update Node.js itself, I recommend you use nvm, the Node Version Manager.