the My Links “vanished” in SharePoint 2010 – they were no longer visible. The Problem: Some clients heavily utilize those server-side favorites.
The links are stored in the Database and the controls to manage the favorites and the page for that is there. Luckily the migration from SP2007 to SP2010 migrated the links, too. Just the control in the ribbon was missing – but there is a very good codeplex solution for that.
In case you are wondering if you could use the links in SharePoint 2013 – the page to manage the links is still there:
One question is open: Are the links migrated from SP2010 to SP2013? I have not tried it yet but I will update this post as soon as I can confirm it.