I have taken over development duties for an eCommerce site. I am considering building a new site from scratch. Is it possible to save the catalog and product listing as they currently exist and import them to the new site? Uploading everything again would be hours of labor.
Is it built into Magento? No it isn't. You'll have to do it manually.
However, there are extensions that can help.
This is the best one by far:
However if you want to rebuild the site, have you thought about going from Magento 1 to Magento 2? There are data imports for that.
To transfer data via database backup-restore if definitely not a solution as it may cause difficulties due to the differences between database structures. The correct way of performing the process will be via export/import.
Moving data to Magento you have to know that by default you can import only products and customers. Attribute sets and attributes, category tree with categories you will have to create/modify manually.There is no out-of-the-box way to transfer order data.
If Source store is not Magento, you will also have to adjust your CSV to requirements Magento has: name column headers in correspondence to database fields, required columns and data in them should be formatted in specific way.
Here is the article on how to transfer data to Magento -
it includes info on how to transfer whole catalog data using Store Manager extension (you can download 2-week free fully-functional version).