Sure you can,
In the Linux world the most popular offering is OpenLDAP...
www.openldap.orgIn the Windows world, Microsoft have a very abused version of LDAP known as Active Directory...
http://www.microsoft.com/windowsserver2008/en/us/active-directory.aspxManaging an LDAP server can be very complicated however, and if your using it for the first time I'd recommend finding a nice GUI to walk you through settings things up. Also address books schema's in LDAP vary depending on the client you'll use to read/write to it.
