While there are many definitions of the word "free" when it comes to the internet, it is important recognize what you are installing on your phpLD directory script, and if there are any requirements. Let's go over some of the main considerations.
First, what type of phpLD license do you own? Anything other than an unbranded license is going to require a link back to phplinkdirectory.com regardless of the requirements of the template. Next, many template designers offer free templates, but there is a requirement to link back to one or more sites in exchange for using the template. And finally, there are some templates that do not require a link back, except as per the phpLD licensing requirements. Here is a list of the templates that do not require any additional linkbacks beyond the licensing requirements:
BlueTheme
Brickster
Celtic Forrest
Chrome
CityScape
Elevation
HorizontalCategories
MotionBlue
Professional
RockAqua
Sandestiny
TerminusGrunge (both versions)
Valentines
If you need these for phpLD 4.0, there is a nice directory template pack here. If you need free templates for other versions, feel free to inquire in our forums.