Many POS terminals send full purchase information back to the cc processor. This is used in fraud detection and also sold as part of your profile.

A while back Mastercard did a commercial where they showed you how you could see what you bought in your online statements.

It looks like this is called "Level 3 data" and primarily for corporate cards, not standard consumer credit cards. I'm not sure if that data is still collected for consumer purchases - I've never been offered any opportunity to see more detail about what I purchased, even for a price.

One significant benefit of having that data would be that it would be easier to remember and prove things you owned for insurance purposes after a loss.