U.S. News posted an article about which career skills every college graduate should learn. I think this list (click on the link for a more detailed description) also applies to graduate students (especially those enrolled in professional programs). I will say these transferable have helped me succeed in my previous positions.
1. Writing clearly and forcefully.
2. Systematizing and organizing data.
3. Doing research.
4. Presenting material orally.
5. Taking notes.
6. Meeting deadlines.
7. Working on a team.
8. Getting along with a boss.
9. Multitasking and time management.
10. Seeing a big project through to completion.
11. Creative thinking.