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Clear NPM's cache:

sudo npm cache clean -f
Install a little helper called 'n'

sudo npm install -g n
Install latest stable Node.js version

sudo n stable
Alternatively pick a specific version and install like this:

sudo n 0.8.20
For production environments you might want to pay attention to version numbering and be picky about odd/even numbers.

Credits

General procedure: D.Walsh
Stable/unstable versions: P.Teixeira
Update (June 2017):

This four years old post still receives up-votes so I'm guessing it still works for many people. However, Mr. Walsh himself recommended to update Node.js just using nvm instead.

So here's what you might want to do today:

Find out which version of Node.js you are using:

node --version
Find out which versions of Node.js you may have installed and which one of those you're currently using:

nvm ls
List all versions of Node.js available for installation:

nvm ls-remote
Apparently for Windows the command would be rather like this:

nvm ls available
Assuming you would pick Node.js v8.1.0 for installation you'd type the following to install that version:

nvm install 8.1.0
You are then free to choose between installed versions of Node.js. So if you would need to use an older version like v4.2.0 you would set it as the active version like this:

nvm use 4.2