It depends upon the incident, the employer and the type of contract that you had. If you left due to feeling that you were about to be fired, it may be the case that your previous employer was trying to force you out via some kind of constructive dismissal. Unless it is a serious incident, employers have to follow a set process of discussing options with you regarding your ability to continue working. Disciplinary procedures also have to be followed before an employee is ever fired. Most above board companies have HR policies which they have to follow for fear of being sued! Why not ask an employment lawyer about your rights ? Alternatively, get a mate with a business to write you a reference as future employers rarely do that many checks. However, this will depend upon the type of industry you are involved in.
Best of luck.