How about astronaught. Entry level , no experience neccessary, requiring Masters…
I can’t think of any that require it as an entrance requirement. But there are jobs that give a pay bump for any masters or require working towards one as a professional development requirement.
Though some academic libraries require the library degree plus an advanced degree in another field - sometimes specified, sometimes not. I know one specific university that will hire people with a non-LIS master’s degree into librarian positions as long as the LS degree is in process. But that doesn’t really fit the OP’s request.
Marketing or Sales or Technical Sales with some medical companies. The Doctorate (Phd) was required because some Doctors (MD) start from the position that all people who aren’t Doctors (MD) are not quite smart enough to take seriously.
Having a Phd says that you aren’t dumb, and the title “Dr” can have a subtle or obvious effect too (yes, sales have been made on that misunderstanding).
The finance example quoted above has some of the same requirement. Rich money brokers assume that anyone who isn’t rich is not quite smart enough to take seriously. In the finance industry it helps balance the negotiations when you go in with the attitude that anyone who doesn’t have a Phd in Physics is not quite smart enough to take seriously.
I don’t believe Einstein had received his doctorate while doing this.
But that was Germany, where evidently they had lower IQ standards for their patent office. 
As DrCube said back in post #10, in the U.S. military, it’s not quite required, but it’s quite standard for officers to get a master’s degree before they can reach O-4 level. It’s not absolutely necessary, but about 80% of those reaching that rank have a master’s degree. There’s no requirement on what subject the degree is in.
This is a good point. At least in the US, a basic requirement for becoming a commissioned officer (O-1) has been having a bachelor’s degree in any subject. You could get this waived if you were a genius tactician or something but it was the basic way in. I know a guy who went to Army OCS (Officer Candidate School) in the 1970’s with a BA in Elementary Education and married a girl who also got a BA in Elementary Education. The guy never actually taught school at all afaik, it was all about the degree (and possibly the girl).
For Spain,
- kindergarten teacher: vocational high school or bachelor’s-equivalent in “Little Children’s Education”
- primary education teacher: bachelor’s-equivalent, preferably but not necessarily in Education or Pedagogy
- secondary education teacher: bachelor’s-equivalent in any field plus a 1-year CAP, “Certificate of Pedagogic Aptitude”, under the pre-Bologna system, or a Master’s in Education under Bologna. Note that the CAP/Master’s qualifies you “to teach secondary school”: having the brains to assign teachers to those subjects they’re actually qualified to teach is supposed to be part of the school director’s job. One of my HS History teachers had a bachelor’s-equivalent in Law and he was the best history teacher I’ve had.
- university: bachelor’s-equivalent (TA), doctorate (professor). Again, the matching of subject to qualifications is a matter internal to schools, and because of the way university works here you often see people teaching subjects where their own knowledge stops where their students’ is supposed to (most of the teachers in a given school will be people with the kind of degrees granted by that school - so, the people teaching math to engineers will be engineers, those teaching math to BS folk will have business degrees, those teaching chemistry to future doctors will be doctors).
In a way, the higher up you get, the less-specific the official requirement.
You probably have to be able to spell it, though.
I think some people covered it, but at least in Oregon and probably a few other states, you need a Master’s degree in SOMETHING (past a certain number of years allowed of teaching with only a Bachelors) but it doesn’t really matter what.
Also, many Peep-ology related jobs will accept a Masters degree in nearly any field, as long as you love Peeps.
physical therapy is now Doctorate only
eventually pharmacy will be this way, to practice you have to earn PharmD.
I would nominate college or university president as well as deans of a college. Most people don’t get high level academic degrees to focus on administration but it is a necessary job and you need a high level degree to lead people under you who have the at least the same level of degree. They can come from any discipline however as long as they have the leadership skills.
Exactly. I suspect this is the nearest anyone will get to answering the OP.
In a university, there is enough professional pride that if you want to be effective beyond a certain level you may need a masters or PhD, simply to have rank with the academic staff you deal with. A PhD helps a great deal. Take it from someone who has been there.
Something I explain to my PhD students - there is a certain mutual understanding between everyone who has got a PhD. It matters less what the subject is than that you made it. That understanding really can make a difference in professional dealings.
Didn’t Homer Simpson once apply? And only got his name right?
In that Steve Martin comedy (The Idiot?) where he was a poor white child and became a millionaire for his eyeglasses, he showed his astronaut application when he applied for a loan.
Not quite any degree, but urban planning, at least in the US, is a profession that generally requires a graduate degree for entry level positions. (Decades ago, a BS or BA was fine. Now, not so much.) Many job listings will include a number of acceptable graduate fields – architecture, landscape architecture, civil engineering, political science, geography, public administration, environmental science – but ultimately, a MUP (Master of Urban Planning) is preferred.
Actually, this was the Swiss Patent Office.
In Germany, this has traditionally been the case with the Foreign Service, i. e. aspiring diplomats.
It’s not a graduate degree, but it could be writing on the wall: McDonald’s cashier position requires a BA.
It appears that those requirements for the McDonalds cashier job are either a joke or a mistake: