How to synchronize Google calender with SharePoint 2010 calender ?
i think this is what your looking for:
also been asked here :)
Hope it helps :)
This very much possible as there are various ways to implement this.
Please check this Link to find out how to achieve this using a tool called Google Calender Sync.
Check this Link to see how to do it using Google API and .NET
Finally a DIY webpart link. But please note this all these need to embed your user id and password, which is not encrypted or completely secure.
Also I would not recommend this for Production sites for obvious reasons.
I guess most options have already been mentioned, but here's my view on this.
Google has an API which you can use to query an online calendar for appointments. If you do so, you can use the SharePoint object model to insert the appointments into a SharePoint calendar. Of course, for syncing you would need to store the original ID of the Google appointment. By the way, I suppose you need a one way sync Google -> SharePoint, if not; things become far more complicated.
The code you'd need to write would a) Query Google's API and get the appointments b) Then get the appointments from your SharePoint calendar c) Compare the two and process the changes in the SharePoint calendar
I would personally create a SharePoint timer job to do this, which you can configure in central administration to run once an hour (or any other frequence you'd might like).
There's no out of the box way to do it, and most tools out there have already been mentioned. So the question than is: do you have the option of custom development, or not?