So I started this out thinking more or less of specific skills that a person should be able to do, but of course the mental side of survival isn't nearly that simple. So what I've kind of come to after reading everyone's posts is there are three rough (and someone overlapping) categories of mental survival skills: mindsets, habits and skills/techniques. I came up with five mindsets and habits and ten skills.

Mindsets:
Face adversity with a can do attitude
Think of your family/love ones and fight to get back to them or keep them alive
Love of the natural world (at least for wilderness survival)
Willingness to learn from mistakes
Keep your head in an emergency (or apparent emergency) and listen to input (even from people you don't necessarily like)

Habits (some of these are also skills, but ones you need to practice constantly):
Cleanliness and organization
Plan
Question everything
Observe
Curiosity

Skills/techniques (these are just the end states, for many I think you should have at least two techniques to achieve the end):
Fire
Meteorology
First Aid
Navigation
Stay warm
Cook
Purify Water/Obtain water
Sew/repair/sharpen
Build shelter
Signal

The skills at least mirror the ten essentials pretty well. Not completely, but basically the same. The skills are also geared toward wilderness survival, but I think they're more or less useful anywhere.