I see tons of solutions for allowing Google Apps to use external AD and LDAP services for login.
However, I already have a ton of users setup in Google Apps already, and I'm trying to go the other way around. That is, I'd like to allow users to log into my external servers using the accounts I created in Google Apps.
Has anyone successfully discovered a way to use a Google Apps domain as an Open Directory, Active Directory, or LDAP provider?
This is absolutely impossible.
Yes, there are means to synchronize between local directory services and Google's directory, but that doesn't mean that you can use Google's directory like AD, OD, or even a simple LDAP service.
Now, if all you want is to enable users to be able to use their Google credentials to sign into your application, look into OpenID.
Note: See answer 4 years after this answer by trs-80 stating that Google introduced a solution.
http://www.nabber.org/projects/oneldap/ provides a backend for OpenLDAP that can at least authenticate users against various services (IMAP, POP, SSH, etc.). It would be possible to write a plugin to use the Google Client Login API directly if you wanted.
This solution would at least work for an app that used LDAP for authentication, but is far from a complete LDAP/AD server.
Google have just released Secure LDAP which does what you want. Note you'll need to have G Suite Enterprise, G Suite for Education or add Cloud Identity Premium to your domain
so basically, you want to have Google Apps act as your domain controller?
I don't think Google Apps has the ability to actually be the DS (directory service). Now, that being said, you can use ADFS 2.0 in your domain to allow those Google Apps users to sign into claims-based applications that you host.
This walkthrough (which goes over extending SharePoint with OpenID logins) addresses ADFS 2.0, SSO, Federation, and all the other principles you need to grasp to make this happen.
I have also been looking at a solution for this and the only thing I can find is this https://jumpcloud.com/
It provides the LDAP and uses the Google directory for user information.