The whole concept of titles and royalty is as old as civilization itself. What is now known as Great Britain is comprised of England, Scotland, and Wales. Add Northern Ireland and you got what is known as the United Kingdom. The Republic of Ireland was once under English rule. England has always been a monarchy, which usually entails princes and a system of nobility.
England's kings and princes go back to the Saxon kings of the 800s. In short, England has rarely been without a monarch on the throne. However, the question remains: do these other countries have princes who hold the same position as the Prince of Wales? Not really. The Prince of Wales is something of a unique title. It once meant a man actually had a ruling position. However, when England conquered Wales in 1300, England's King Edward I named his infant son and heir, Prince Edward, the title. It has since been bestowed on the male heir apparent to the English throne.
The title is not hereditary, however, and cannot be passed down. The monarch must "invest" the heir with the title, as Britain's Queen Elizabeth II invested her son, Prince Charles, with the title. If Charles ever ascends to the throne, it will be at his discretion whether to invest his son, Prince William, with the title. Otherwise, it would remain vacant.
Princes are still known widely in England, but not in the other countries of Great Britain. Princes are generally direct relatives or descendants of the monarch: siblings, grandchildren, nieces, nephews, etc. While there are members of the nobility in Scotland and Wales, only royalty are princes. Queen Elizabeth has not chosen to create a title or style such as "Prince of Scotland" or "Prince of Ireland," nor is it likely that she would.
One interesting thing about princes and their titles is that princes may be dukes or earls, or hold other titles, but dukes and earls are not necessarily princes. The Prince of Wales, for instance, is also the Duke of Cornwall and the Baron Renfrew. This is why his wife, Camilla, is known as the Duchess of Cornwall. The title Princess of Wales still belongs to the late Diana, first wife of the Prince of Wales, and mother to the heir. She will always be known by that title, even when the next Prince of Wales marries and his wife acquires that title.
There are numerous excellent reference books on the subject of British royalty and nobility, as well as Internet sites devoted to it. One good place to begin looking for information is www.royal.gov.uk — the British royal family's official Web site.