Is it possible to use Infopath 2010 forms with Sharepoint Foundation 2010? What licence(s) (if any), would I need to do so?
InfoPath forms requires SharePoint enterprise edition as the form server component is a part of it. With SharePoint foundation or SharePoint standard you can use your lists as forms. If that's not enough, try to use forms solutions above lists. A simple search provided these solutions:
Look at SharePoint Forms Designer, it works with SharePoint Foundation as well as SharePoint Server.
You need to have a licensed version of SharePoint Enterprise ,as the form service are part of enterprise. After that, you need to use stsadm command and activate the feature IPFSAdminWeb ,you will be able to see the in central admin -> general app settings. Very important , if you need to use infopath forms , always create the form at the root site , else infopath gives error connecting to site