Basic AI drives
For the most part, whatever your goals are, choosing in accordance with decision-theoretic desiderata will help you achieve them, and so despite the vast diversity of possible minds, we have theoretical reasons to expect that AIs that have undergone substantial self-improvement will tend to share certain features. Steve Omohundro has identified several of these Basic AI drives. Goal-seeking agents will usually strive to represent their goals as a utility function, prevent "counterfeit" utility, protect themselves and similar agents, and acquire resources.
Obviously, AIs whose goals directly contradict these basic AI drives will strive to avoid them.