Is it possible to display the standard home page component such as tasks, calender and dashboards on a visualforce page?
Regarding - Dashboard snapshot in VF page. Read the SFDC Help pages to "Embed Report Charts in Visualforce Pages". and the relevant visualforce tag page. Please note this feature is only generally available from the Spring '14 release.
They're actually always displayed if you don't put sidebar="false" in the apex:page parameters. But that's probably not what you mean?
Since these are not part of the VF library I don't think you can add them to a VF page. They're not that complex, though, so most of it you can probably rebuil from scratch in VF if you really want to.