XenForo_Session - Custom "remember me" handling & extending session timeouts. Somewhere there's a feature request to allow better extending of this class instead of all of the static method calls.
XenForo_ControllerPublic_Abstract - Performance of banned & discouraged IPs.
XenForo_ContentPermission_Node - Optimizing permission rebuilds for large number of nodes. We changed this in an IGN specific way so I haven't submitted a patch to XenForo.
XenForo_Template_FileHandler - Removed "final" from some methods
I also modified these two classes but I don't really count this as modifying the core XenForo since it is just for debugging or logging purposes.
XenForo_Error - added logging to NewRelic for errors
XenForo_Debug - Added logging to say if the query was against the master or slave db server