I have a LAMP configuration setup on 2 linodes. One is a web server, the other a DB. Do I have to pay for bandwidth between my linodes? They are both at the Fremont CA location.

As long as you bring up a private IP on both nodes and use that private IP to communicate between them, you will not be charged any bandwidth usage.

This might help too:
http://library.linode.com/networking/co ... nterfaces/

But, if I just use the public IP addresses for communication between them, I will have to pay for bandwidth?

Yes. To not use up your bandwidth you have to use the private network.

Excellent, thank you for the clarification.

Can I use private addresses between linodes on different accounts? For company structure/billing purposes we have a couple of different linode accounts with containers in them. Can I use private addresses to communicate between containers in the different accounts?

As long as you're using the private network IPs, then yes, it's free.

There's a bunch of internal services that you can use from others like that:

https://www.linode.com/wiki/index.php?t ... l_Services

Absolutely.

In fact, there are a number of people (myself included) who offer various services (NTP, apt caches, etc) to other Linode customers via the private network.

Nice. Thanks for the clarification. This opens up a number of possibilities for us.

Just to reiterate, the linodes have to all be in the same datacenter. Your OP says they're all in Fremont, but if you add another elsewhere, you won't be able to use the private network.