The Plantagenet Dynasty
Formed with the marriage of Matilda, daughter of King Henry I to Geoffrey Plantagenet, Count of Anjou, the Plantagenets succeeded the Normans, and were succeeded -- after the battling houses of Lancaster and York, and The War of the Roses -- by the Tudors. Geoffrey's nickname, Plantagenet, refers to a sprig of genet or broom he habitually wore in his cap.
With the Plantagenets, Medieval Britain began to emerge from the dark ages of the Normans to establish the very beginnings of a cultural heritage: the emergence of Gothic architecture; the language enriched by contact with the French; the establishment of more effective governmental and judicial systems; the universities of Oxford and Cambridge, and towards the very end of the period, the poetry of Geoffrey Chaucer. At the start of the period, there remained close ties with Anjou, but these hereditary Angevine holdings were mostly sold by Henry III to pay off his debts.
More in-depth histories belong with each individual King, but here's a rough summary of the juicy bits.
When Henry II came to power, marrying Eleanor of Aquitaine, it is as one of Europe's most powerful monarchs, his Empire extending from the North of England down to the Pyrenees. Henry actually restored the territories lost to the Scots by previous monarch Stephen. He is a great leader, tireless and forever on the move, a soldier and a scholar. It is he who revolutionalises the legal system, introducing common law, aspects of which remain with the British legal system even today.
Richard I spent most of his time fighting the Crusades, reportedly spending just 6 months of his 10 year reign in England; he still held his territory, but his great wealth quickly vanished. King John has gone down in history as the real bad egg, losing Normandy and the majority of other territories in what is now France. A variety of politically unsound moves in France lead to him alienating almost everybody; he fled to England, where civil war was only narrowly avoided with the signing of the Magna Carta in 1215.
Henry III acheived the throne at the age of 9, and so affairs are governed by his regents until he reaches 25. An extravagant King, he ran into great debts with his program of church building, and pursuit of war against Wales and France; he became unpopular amongst the nobility, choosing to bestow favours upon foreigners instead, and after several failed reforms, the baronials led by Simon de Montfort rose against him during civil war in 1264.
Edward I's reign was a great and eventful one; he had the strength and determination his father lacked, coupled with a strong sense of community. Immediately he set about restoring order to the corrupt barons and royal aides, with a huge move to restore justice to the land. Beginning by taking control over Wales with a bit of cunning and rather more brute force, his later attacks on William Wallace's Scotland were eventually successful but nevertheless ill-fated. Edward removed the legendary Stone of Scone to London, where it was placed in the Coronation Chair in Westminster Abbey and remained there up until 1996. The new government formed in Scotland included Robert the Bruce, whose rebellion in 1306 allowed him to regain control during Edward II's reign.
Edward II is a miserable ruler, and it is up to Edward III to restore royal prestige again. Despite courage and charisma, there is still devastating social disorder with the outbreak of bubonic plague (the 'Black Death'.) His attempts to take control of parts of France saw the beginnings of the Hundred Years War in 1336; he did well in the first battles, but later failed by continuing to fight even when half his army are crippled with plague. Richard II eventually pursued a policy of peace with the French; at 29, he married the 7 year old Princess Isabella of France to stop further struggles.
Richard had no children, and with his death, the split Plantagenet line continues, first with the Lancastrians and then the Yorkists. The War of the Roses plunges Britain once more into chaos.