Standards for Conviction
In almost every country in the world a defendant is presumed innocent until they plead guilty or are proven guilty at a trial. What is the standard required to prove an individual guilty of a crime? The exact standard is sometimes difficult to define but countries generally use one of two standards: Proof Beyond a Reasonable Doubt or Preponderance of the Evidence.
Courts are often reluctant to define Proof Beyond a Reasonable Doubt as a percentage probability. A jury may be given specific instruction as to the precise meaning of the term in their jurisdiction. It is generally considered to be a very high standard but one that is theoretically achievable by the prosecution.
Presponderance of the Evidence is a standard easily defined as simply more probable than not. It is the standard used in some civil law countries.
In either case, the prosecution has the burden of overcoming the defendant's presumption of innocence. As a result, both systems will generally hold that doubts should be resolved in the defendant's favor. In Continental systems, lawyers will sometimes state this as the maxim, in dubio pro reo.
Criminal v. Civil Liability
Both standards may exist in the same jurisdiction for different types of cases. For instance, in the United States, Proof Beyond a Reasonable Doubt is the standard for criminal conviction while Preponderance of the Evidence is used to determine liability for civil cases. Thus, it is possible that an individual aquitted of a crime can still be found liable in a civil case.
The famous case of O.J. Simpson provides an illustration: Mr. Simpson was accused of murdering his wife, Nicole Brown Simpson. A jury determined that Mr. Simpson was not guilty of the crime and that the prosecution had failed to prove its case beyond a reasonable doubt. However, a separate civil jury was convinced by a preponderance of the evidence that he was responsible for the murder of Nicole Brown Simpson and awarded her family $8.5 million in compensatory damages.
Country Specific Applications
Proof Beyond a Reasonable Doubt is the standard required in the United States for conviction of a criminal charge. The standard is generally not quantifiable as a percentage probability. The exact formulation of reasonable doubt has never been determined.
Chief Justice Shaw of the Massachusetts Supreme Judicial Court made this observation about the reasonable doubt standard in 1850:
"[W]hat is reasonable doubt? It is a term often used, probably pretty well understood, but not easily defined. It is not mere possible doubt; because every thing relating to human affairs, and depending on moral evidence, is open to some possible or imaginary doubt. It is that state of the case, which, after the entire comparison and consideration of all the evidence, leaves the minds of jurors in that condition that they cannot say they feel an abiding conviction, to a moral certainty, of the truth of the charge. The burden of proof is upon the prosecutor. All the presumptions of law independent of evidence are in favor of innocence; and every person is presumed to be innocent until he is proved guilty. If upon such proof there is reasonable doubt remaining, the accused is entitled to the benefit of it by an acquittal. For it is not sufficient to establish a probability, though a strong one arising from the doctrine of chances, that the fact charged is more likely to be true than the contrary; but the evidence must establish the truth of the fact to a reasonable and moral certainty; a certainty that convinces and directs the understanding, and satisfies the reason and judgment, of those who are bound to act conscientiously upon it. This we take to be proof beyond reasonable doubt." 
In the U.S. Supreme Court case of Victor v. Nebraska , the court held a similar jury instruction on reasonable doubt unconstitutional:
" `[A reasonable doubt] is one that is founded upon a real tangible substantial basis and not upon mere caprice and conjecture. It must be such doubt as would give rise to a grave uncertainty, raised in your mind by reasons of the unsatisfactory character of the evidence or lack thereof. A reasonable doubt is not a mere possible doubt. It is an actual substantial doubt. It is a doubt that a reasonable man can seriously entertain. What is required is not an absolute or mathematical certainty, but a moral certainty.' "
The court held that the portions of the instruction in bold rendered it unconstitutional. The court has never fully approved an instruction.