With this free tool, You can connect to a SharePoint site and download the documents and lists to your local machine and access them offline. There is another product from the same vendor, Colligo Contributor, which allows two-way sync with SharePoint and which is not free.
By the way, we have SharePoint Workspace 2010 (which is the successor of Microsoft Office Groove 2007) which supports two-way sync but not a free product.
Download URL: https://www.colligo.com/products/colligo-briefcase/
Disclaimer: By writing this, I’m not endorsing this product by anyway 🙂