(Hope the thread visitors don't mind a little out-there dreaming about what could be next)
One thing that might be cool is giving Cortana facial expressions even when users are not actively interacting with her, and using that to prompt natural interaction. I think this is technically feasible:
Example: Cortana is rendered on the screen in low power mode (think 'glance screen') with no or little animation. If a user has indicated an interest in news, Cortana would track news items throughout the day and use related twitter posts to extract whether the news is sad, funny, or exciting. Then when the phone senses that the user picks it up, Cortana could look worried, or flash a smile, depending on the type of news. This would prompt natural conversation along the lines of 'what's so funny' or 'why are you smiling'. She could respond '
I just read that [insert funny news item from preferred sources]'. An extreme case that would surely stir up a lot of hype is if a particularly tragic event would cause the avatar to cry, but run that by the PR team before implementing.
What I like about this general idea is a) that it's using readily available tech, b) that as described does not cause a lot of battery drain, and c) that this would make her sort of a humanized version of the internet, providing information of interest to the user in a natural way, but (in this mode) only if the user asks.