It is a common error that users generally encounter when they try to execute a brew command as sudo and shown below is an example of how the error looks like:

Debjit-Sahas-Mac-mini:mcrypt debjit$ sudo brew link mcrypt
Password:
Sorry, try again.
Password:
Error: Cowardly refusing to `sudo brew link`
You can use brew with sudo, but only if the brew executable is owned by root.
However, this is both not recommended and completely unsupported so do so at
your own risk.

UPDATE: if you are facing permission issues with HomeBrew on Mac OS X El Capitan, then you should read this.

There is a simple fix associated with this. Just go ahead and execute the following four commands in that order:

Homebrew Logo - Mac OS X

First find out what is the current ownership of the installed package of brew (you will need this info in the last step)

ls -al `which brew`

Change the user and group of brew to root and wheel respectively:

sudo chown root:wheel `which brew`

Now execute your brew command as root, for eg. sudo brew link mcrypt. Lastly, revert back the ownership of brew to what you had found out in step 1 above

sudo chown : `chown brew`