Previously, you could deal with this using SSL tunneling, but that has been deprecated since the retirement of LDAPv2 (in 2003). TLS is another option, but even using that, LDAP still has security problems.
For security, your best option is Kerberos. Kerberos is specifically designed to handle authentication. It will not do the information lookup that LDAP does. It avoids password security problems and enables single-sign-on (a very useful feature!).
So the ideal situation is to use both Kerberos and LDAP: one for authentication and one for information organization and access. In fact, they do play quite nicely together, but information about on how to achieve this is limited. If you do want to set them up, check out this two-part article I wrote (requires registration but is free) a while back which is still relevant. You can also get more information from the LDAP and Kerberos web pages.