The Webmasters FAQ outlines the nature of acceptable questions for this site: researching available solutions and providing anecdotal advice falls outside the purpose of this StackExchange site, so this type of question would be better-suited to chat or another discussion forum.
That being said, there are a variety of free and open source ecommerce systems, as well as licensed software and paid services, which may meet your requirements.
Some of the most popular ecommerce scripts include:
All of the ecommerce scripts listed above are built around the concept of mods (plugins) which extend the application's functionality - there are many mods, with new mods authored every day.
If you have researched different ecommerce scripts and available mods but cannot find anything that will meet your needs, you should consult a developer (or do it yourself) who can build something to your specifications either as a mod for an existing ecommerce script or as a stand-alone application.