I have about 15 automotive related websites (each site has a different
supplier). And all of them have a links page that links them together.
Example - "Need parts for any other makes" and then has the sites
listed.
I am not linking to any other sites other than my own. I was told this
was called a closed loop and I would get penalized for this. Is this
true? Should I not link them together?

Hello, apn:

 If by get penalized you mean that someone is going to call you at
night telling you not to do so, no, no one it's going to do it because
it's not illegal do that with your own sites. So let's look more in
depth what is "closed loop linking" or better said, "cross linking".

Here you have some posts about it:

Cross Linking Question
http://www.webmasterworld.com/forum3/9360.htm

Linking a circle of web sites
http://www.webmasterworld.com/forum3/15696.htm

Google's Page Rank system penalizing for crosslinking?
http://www.webmasterworld.com/forum3/4618.htm

The only "penalization" you can get is from Google's Page Rank system,
because if you cross link sites, and due the Google's Page Rank system
way of work, this will make your sites have a higher ranking, and
Google prevent this "false" ranking by penalizing those sites. That's
all. There is not an official response from Google that they do that,
but there are many sites that have been penalized.

Also read this forum message, it's very interesting:

Crosslinking and Google
http://www.cre8asiteforums.com/viewtopic.php?t=420

I hope this helps, in any case, don't hesitate to request for any
clarification.

Search strategy

google crosslinking
://www.google.com/search?hl=en&lr=&ie=UTF-8&oe=UTF-8&q=google+crosslinking&btnG=Google+Search

"closed loop" linking page
://www.google.com/search?hl=en&lr=&ie=UTF-8&oe=UTF-8&q=%22closed+loop%22+linking+page&btnG=Google+Search

Regards.