Most legal systems provide for a right of initial appeal to at least a first tier of appellate or reviewing courts without the need to make any special request or application, provided the lower court or agency proceedings are finished. Appeals to higher levels of appeals courts, or more substantial appellate proceedings (e.g., United States en banc appeals), and appeals before the lower court or agency proceeding is finished (i.e., interlocutory appeals) may not be as-of-right, but instead may require permission from either the appellate court (e.g., certiorari) or from the court from which the appeal is being made.
Most notably, in U.S. practice, appeals to the United States Supreme Court are almost always not as-of-right.