Questions about termination
There are basically two ways to leave an academic program permanently: withdrawal and termination. 


Withdrawal is a voluntary process, which can occur for any of a number of reasons: academic dissatisfaction, financial, psychological, medical, or family are usually the most common of these. The key factor here is that withdrawal is normally initiated by the student. It is "neutral" in the sense that normally the student hasn't done anything wrong, and could have continued in the program had she so chosen.
Termination is an involuntary process initiated by the supervisor or department. Usually, under such cases, the reason is inadequate performance or violating departmental policies. For instance, one might fail a qualifying examination, fail to pass required courses, committed "academic dishonesty," or violated some other regulation. This is the sort of "black mark" that you are referring to. Depending on the situation, this can have catastrophic effects on the student's ability to apply and be accepted elsewhere. It all depends on the nature of the situation, and what the student's role in the situation was.


On the other hand, suspension or probation are serious issues that require disciplinary action but are not so serious as to require termination. Probation may or may not need to be reported, but an action which leads to a suspension—or temporary removal from the graduate program—probably would need to be reported, if asked about it.

It is not necessarily a given if you will be asked about this in a graduate application—it depends very much on the particular program or school to which one applies.