If you just want to fix the issue quickly, scroll down to the "solution" section below.

If you're a Mac Homebrew user and you installed node via Homebrew, there is a major philosophical issue with the way Homebrew and NPM work together. If you install node with Homebrew try to do npm update npm -g, you will see error like this:

$ npm update npm -g
npm http GET https://registry.npmjs.org/npm
npm http 304 https://registry.npmjs.org/npm
npm http GET https://registry.npmjs.org/npm/1.4.4
npm http 304 https://registry.npmjs.org/npm/1.4.4
npm ERR! error rolling back Error: Refusing to delete: /usr/local/bin/npm not in /usr/local/lib/node_modules/npm
npm ERR! error rolling back     at clobberFail (/usr/local/Cellar/node/0.10.26/lib/node_modules/npm/lib/utils/gently-rm.js:57:12)
npm ERR! error rolling back     at next (/usr/local/Cellar/node/0.10.26/lib/node_modules/npm/lib/utils/gently-rm.js:43:14)
npm ERR! error rolling back     at /usr/local/Cellar/node/0.10.26/lib/node_modules/npm/lib/utils/gently-rm.js:52:12
npm ERR! error rolling back     at Object.oncomplete (fs.js:107:15)
npm ERR! error rolling back  [email protected] { [Error: Refusing to delete: /usr/local/bin/npm not in /usr/local/lib/node_modules/npm] code: 'EEXIST', path: '/usr/local/bin/npm' }
npm ERR! Refusing to delete: /usr/local/bin/npm not in /usr/local/lib/node_modules/npm
File exists: /usr/local/bin/npm
Move it away, and try again. 

npm ERR! System Darwin 13.1.0
npm ERR! command "/usr/local/Cellar/node/0.10.26/bin/node" "/usr/local/bin/npm" "update" "npm" "-g"
npm ERR! cwd /Users/dan/Google Drive/Projects/dotfiles
npm ERR! node -v v0.10.26
npm ERR! npm -v 1.4.3
npm ERR! path /usr/local/bin/npm
npm ERR! code EEXIST
npm ERR! 
npm ERR! Additional logging details can be found in:
npm ERR!     /Users/dan/Google Drive/Projects/dotfiles/npm-debug.log
npm ERR! not ok code 0

There's an NPM bug open for this exact problem and a long thread that is still actively being debated, but the summary is that npm is its own package manager and it is therefore better to have npm manage itself and its packages instead of letting Homebrew do it. Also, using the Homebrew version of npm requires sudo to install global packages. That's also a very bad idea.

This solution fixes the error caused by trying to run npm update npm -g. Once you're finished, you also won't need to use sudo to install npm modules globally.

Run the following commands to remove all existing global npm modules, uninstall node & npm, re-install node with the right defaults, install npm as its own pacakge, and configure the location for global npm modules to be installed.

rm -rf /usr/local/lib/node_modules
brew uninstall node
brew install node --without-npm
echo prefix=~/.node >> ~/.npmrc
curl -L https://www.npmjs.org/install.sh | sh

Node and npm should be correctly installed at this point. The final step is to add ~/.node/bin to your PATH so commands you install globally are usable. I added this line to my ~/.path script, which gets called via ~/.bash_profile. If you want to see a full example you can check out my dotfiles repo on github.

export PATH="$HOME/.node/bin:$PATH"

You'll need to re-install your global node modules again. As an example, a few I use are:

npm install -g grunt-cli http-server uglify-js jshint yo nodemon