Recommendation letter from a supervisor after falling out In the event of a falling out with a supervisor (Master's thesis or PhD) is there generally anything one can do about it if one wants to apply to a (different) PhD program, for which one would need a recommendation letter? I am mostly interested in the European academia. 

I am certain this must have happened a lot in the history of academia and I am wondering what happens in such situations. Is it the end of one's academic career? Are the other options to leaving or (if possible) changing research groups within the university? I know that one can't force a person to write a positive letter, but is there anything that outsiders can do to effect such a situation or is all the power with the supervisor?
To begin with, most supervisors are reasonable, decent people.  So, the option of communication, depending on the nature of the falling out, is quite reasonable.  It is perfectly possible to finish a PhD with a substantially acrimonious relationship.  It might be best to study communication skills a bit first.

If that isn't practical, typically, the former supervisor has a lot of power.*  However, very few things are absolutes.  The purpose of a supervisor's letter is to gain insight from someone who has previously worked with you.  In the USA, in my experience, a certain amount of creativity is acceptable as long as you can fulfill that purpose.

For example, my PhD supervisor switched continents and became quite busy with startups without leaving a forwarding address...  So, I provided a letter of recommendation from another supervisor along with a note describing the circumstances for some fellowship applications.  No problems. Albeit, I worked in research in industry for several years.

*One thing many graduate students overlook is properly researching potential advisors.  The cost of a PhD, typically, significantly exceeds the price of a home.  And, typically, is much riskier.  Yet, somehow, students jump into PhD programs far more easily than they'd buy houses.  On the positive side, in departments I have been in, there have been a few supervisors with known personality issues and, within the department, accommodations were made for students leaving those groups.