ClickCartPro and EuropaCart integrate with Joomla! via a series of extensions to provide Joomla! template imports, skin widget exports and single sign on functionality.

The integration between our shopping cart software and Joomla! is very unique in that our software and Joomla! 1.5.x run in parallel on the same domain as two standalone installations. Each is installed separately and is independent of the other. With all extensions installed and activated you get:
You'll see all three of the integration functions detailed above working in the demo linked to below. What you get in this demo is our software and Joomla! connected and using single sign on. Joomla! is importing several skin widgets from the online store and is using the Joomla! JA_Purity template. The online store is importing the Joomla! template as it's skin on each page load to maintain the look and feel of both systems.
As we configured the demo, we suppressed the Joomla! login and registration pages and included the online store pages in the menus. We think it works best this way - but you could technically suppress the online store login/create account menu links in favor of the Joomla! ones. If you do this, when users created in Joomla! checkout in the store, they will be asked for all the info they didn't complete when signing up for their account in Jooma! (like their location, contact info, subscriptions, etc.). Regardless, users created in one system are added to the other. This integration won't break because you have a special module on your registration page. It plays really nice with Joomla! and vice versa.
We have created an article in the Software Wiki which will help you configure your online store to communicate with Joomla! 1.5.x. Simply follow the steps outlined in the wiki article which covers installing Joomla!, installing ClickCartPro or EuropaCart, and configuring each to work together.