Before You delete Your account, don't forget to delete Your family site, if You don't delegate the site manager role to any other member in Your list.
You can delete the family site by clicking on Your profile and then click on Site settings and there on the General link. Now click on the Administration tab and there click on the button Delete my site.
You can delete Your account in Your profile (see upper right corner on the browser window. Click on My profile and then click on Edit account. There is a link at the bottom called Delete my account.