Cortana running in background

For me I keep her on so I can:
Have an easy way to create calendar appointments from texts and emails since she reads them and will highlight any information.
So I can create quick location/people reminders. I love being able to remind myself to pick up something the next time I'm at The Home Depot.
I like the live tile with news and weather updates.

I can't think of anything else besides the actual use of Cortana, I'm sure there are others out there with their own reasons.
 
You also forget that she can track flights, track your location to and from your favorite places, especially for location based reminders.

There are other examples too, but that's enough.
 
At the moment there may not be a whole lot you can do by letting Cortana run in the background, however more features will come.

Currently Cortana periodically keeps checking your location to see if you've set any reminders for a specific location, it also updates th live tile every few minutes to alert you of breaking news or any odd weather patterns.

In the future there may be an ability for you to turn Cortana by saying a keyword even when the phone is locked, the keyword could be something like 'Hey, Cortana', but no one knows for sure.

It is worth noting that some people are experiencing battery issues by letting Cortana run in the background(and with the live tile.)
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Thanks for that :) I also discovered that if you set a reminder to pick up milk from a shop then Cortana won't work if background is turned off. She will tell you that too. So there was more to it then I thought. I will keep her on tho as I am guessing it will allow her to track my regular journeys and learn more about me and assist in short cuts and the such