Edward (Edward II) 1284-1327, was the first English Prince of Wales, imposed on the Welsh by his father (Edward I) (with the slightly specious claim that he was born in Wales - in the English held castle of Caernarvon), created Prince in 1301 (although the intention to give an English prince the title was probably made earlier at time of the defeat of Llywellyn, the last Welsh prince, in 1282).
The title has been held by heirs apparent to the monarch, usually by the son of the monarch, in two cases by grandsons. The title is not automatically given to the heir, unlike the Duchy of Cornwall which is inherited at birth.
Edward II reigned (1307-1327), defeated by the Scots at Bannockburn (1314), continually in dispute with his barons, who resented his favourites, Piers Gaveston and, later, Hugh Le Despenser. Finally he was deposed and probably murdered, horribly, (although some reports say he survived, living as a hermit).
Edward III (1312-1377), the son of Edward II was never created Prince of Wales. He reigned from 1327 to 1377. His claim to the throne of France started the Hundred Years War, in which Edward III was victorious at the battles of Crecy and Poitiers.
Edward the Black Prince (1330-1376), the son of Edward III, created Prince of Wales 1343, died, presumably of the Black Death, before his father, (his own eldest son, also Prince Edward, died in 1370).
Richard (1367-1400), (Richard II), son of Edward the Black Prince, created Prince of Wales 1376, reigned from 1377 to 1399, when he was deposed (by Henry IV, Bolingbroke) and probably murdered in 1400.
Henry of Monmouth (Henry V), (1387-1422), son of Henry IV, created Prince of Wales in 1399, reigned from 1413 to 1422, dying at the age of 35. He continued the Hundred Years War, winning battles including Agincourt.
Henry VI (1421-1471), son of Henry V, was never created Prince of Wales, he reigned from 1422 to 1461, and briefly from 1470 to 1471, when he was finally deposed and eventually murdered, at the end of the Wars of the Roses. The Hundred Years War ended in his reign, with France eventually reclaiming all the territory gained by England.
Edward (1453-1471) (Son of Henry VI), created Prince of Wales 1454, was killed after defeat at the battle of Tewkesbury.
Edward (1470-1483) (Edward V), son of Edward IV, created Prince of Wales 1471, one of the "Princes in the Tower", almost certainly murdered on the orders of Richard III (or possibly Henry VII).
Edward, son of Richard III, created Prince of Wales 1483, died young in 1484, during the short reign of his father.
Arthur Tudor (1486-1502), son of Henry VII, created Prince of Wales 1489, died before his father.
Henry Tudor (1491-1547), Henry VIII, son of Henry VII, created Prince of Wales 1503, reigned 1509-1547.
Henry VIII had several sons (by Catherine of Aragon) all of whom died in infancy. None of these formally became Prince of Wales; it is possible that one of them was informally referred to by the title.
Edward VI (1537-1553), son of Henry VIII (by Jane Seymour), was never created Prince of Wales, he died after a short reign (1547-1553).
A full century passed before another Prince of Wales was created, as the Tudor queens had no heirs apparent.
Henry Frederick Stuart (1594-1612), son of James VI and I, created Prince of Wales 1610, died before his father.
Charles Stuart (1600-1649) (Charles I), second son of James VI and I, created Prince of Wales 1616, reigned from 1625 to 1649, when he was deposed and executed at the end of the English Civil War.
Charles Stuart (1630-1685) (Charles II), son of Charles I, declared Prince of Wales 1638, exiled during the Commonwealth, restored as King in 1660 after the death of Oliver Cromwell and the resignation of Richard Cromwell, died in 1685 with no legitimate descendent (the Duke of Monmouth, his illegitimate son, attempted and failed to seize the crown from James VII and II (the brother of Charles II)).
James Francis Edward Stuart (1688-1766) (the Old Pretender), son of James VII and II, declared Prince of Wales 1688, his father was deposed in 1688. He failed to take the crown in the 1715 rebellion, as did his son Charles Edward Stuart in the 1745 rebellion. James VII and II had several elder sons who died in childhood and before his accession.
None of the many children of Queen Anne survived until her accession. Her last surviving son died in 1700, two years before she became queen.
George Augustus (1683-1760) (George II), the son of George I, created Prince of Wales 1714, reigned 1727 to 1760.
Frederick Louis (1707-1751), son of George II, created Prince of Wales 1729, died before his father.
George William Frederick (1738-1820) (George III), grandson of George II, created Prince of Wales 1751, reigned from 1760 to 1820, eventually illness and insanity compelled his retirement and the Regency of his son.
George Augustus Frederick (1762-1830) (George IV), son of George III, created Prince of Wales 1762, Prince Regent 1811-1820, reigned 1820-1830; his (morganatic and possibly unlawful) marriage to Maria Fitzherbert was declared null; his marriage to Princess Caroline of Brunswick was not happy, and George prevented her coronation as queen; his daughter Princess Charlotte died in 1817 during the Regency.
Albert Edward (1841-1910) (Edward VII), son of Queen Victoria, created Prince of Wales 1841, reigned 1901 to 1910. His eldest son, Albert Victor, Duke of Clarence, died in 1892, before Queen Victoria.
George (1865-1936) (George V), son of Edward VII, created Prince of Wales 1901, reigned 1910 to 1936.
Edward (1894-1972) (Edward VIII), son of George V, created Prince of Wales 1910, reigned in 1936, but compelled to abdicate.
Charles (1948 -) , son of Elizabeth II, created Prince of Wales 1958, (the formal investiture was in 1969).
A quick count shows (of those who actually took the title):
Never inherited the crown - 7
Became king, but were deposed - 6
Became king, but was effectively retired - 1
Became king, retaining the crown until their death - 7