Ok, so this answer works for the Anaconda 64bit Python distribution with ArcGIS 10.1 64bit on Windows 7/Windows Server
First, install anaconda, it should go to the directory C:\Anaconda. Check the box 'make system default python'. It may give a warning that there is another python installed, but continue. Then:
First thing to do is to copy over the DTBGGP64.pth file to the new distribution directory (C:\Anaconda) from C:\Python27\ArcGISx6410.1\Lib\site-packages.
This will allow you to import ArcPy when using the new distribution.
Next, the environment variables must be checked:
In the system variable Path, there needs to be the following paths, in this order: C:\Python27;C:\Anaconda;C:\Anaconda\Scripts.
C:\Python27 must come before the path to the new python distribution.
If there is a User Variable called PYTHONPATH, this should be deleted.
Finally, the registry keys must be checked. Normally there should be nothing to change but it is worth double-checking.
Check the following keys:
There should be one key and its’ value should be C:\Anaconda\Lib;C:\Anaconda\DLLs
The key should be C:\Anaconda
The PythonDir key should be *C:\Python27*
Arc's Toolboxes and integral Python console should now work fine, and you should also be able to import arcpy (and all the other 3rd party packages) from the external console(s) given with Anaconda (Spyder/Ipython etc..)
I imagine that the process would be similar for installing Python(x,y) etc.