This Forbes editorial piece says none...

http://www.forbes.com/sites/johntamny/2013/02/10/sorry-left-and-right-no-job-requires-a-college-degree/

So, which ones really require it?

I think trade schools would be far more effective. Colleges are really only good for making well rounded people who have touched alot of subject, perhaps for philosphers. Other than that a more focused trade school could turn out better workers cheaper and faster than colleges as they wouldn't need all the extra classes.

A prostitute.

Research Scientist. Without a doubt.

What I got from that.

"Being smart is a function of curiosity that decidedly cannot be taught."

Now we just need to get rid of the importance placed on that piece of paper.

Some parents don't treat us that way.  Though my young age isn't helping get through to them.

Or maybe its a High School thing.....

engineering, medicine, law

Accounting

That you need the knowledge gained on the degree to do the job:

Scientist
Lawyer
Doctor
Teacher (only the postgraduate training)

That require a degree anyway

Engineer
Military Officer
Management
Banking

Strippers.