Sweyn Forkbeard and Hardicanute we share with Denmark, and Canute the Great with Denmark and Norway (and also part of Sweden). How this happened was Sweyn of Denmark (whose grandmother Thyra was a niece of King Alfred of the English) invaded to avenge the death of his sister Gunhilda (she and her husband, and many Danes, had been killed on the orders of King Athelred) and to drive Athelred from the throne. He received submission of the whole north and midlands before marching on London, where he was proclaimed King (and Athelred fled to his brother-in-law in Normandy). Sweyn ruled both Denmark and England briefly, for he died a few weeks later.
His son Canute inherited both Denmark and England (in fact he was King of England before he ruled Denmark, since his brother Harold II was ruler of that kingdom until his death in 1018, on which Canute gained both realms), and later conquered Norway and part of Sweden from Olaf II (St. Olaf). Canute also married Athelred's widow.
When Canute died he gave England to his son (from his first marriage) Harold, and Denmark to his son Hardicanute (who was born from the union with Athelred's widow, his second wife). Hardicanute ruled Denmark as Canute III, and after his half-brother's death inherited the English throne in 1040.
The next nation is Ireland. All English kings from John to Henry VII were given the title Lord of Ireland, and King of Ireland from Henry VIII until George V, when it gained independence. This goes back to 1167, when King Dermot MacMurrough of Leinster was deposed by Rory O'Connor, King of Connacht and High King of Ireland. Dermot petitioned Henry II of England to help him regain his throne, and Henry's army (commanded by Earl Richard 'Strongbow') invaded Leinster, with Strongbow marrying Dermot's daughter Eva. When Dermot died, Strongbow's descendants through Eva inherited lands in Leinster; and, with the Pope's backing, Henry invaded Ireland for a second time with the purpose of gaining control over his vassals' Irish lands. The isle was given to him as a papal fief (i.e, a 'lordship'), which Henry gave his youngest son John (who had no lands or titles of his own). John's successors ruled the area around Dublin in the 'Lordship of Ireland'.
Originally, the dominions were kept distinct, but when John ascended the English throne in 1199 on the death of his older brother Richard, he kept both titles. And so all Kings of England, beginning with his son, were also styled Lords of Ireland. When Henry VIII broke with Rome, he could no longer hold the lordship as a papal fief, and so styled himself as 'King of Ireland', and his successors began a full invasion beyond the boundaries of Dublin and the Pale. Over time more kings began accelerating the colonisation of the Gaelic regions, most notably after the Union of England and Scotland when James I and VI started settling border reivers and Scottish Presbyterians in Ulster.
Wales, prior to Henry VIII's incorporation of it into England, was technically a semi-independent principality. It had been united from various smaller kingdoms into a principality under Llywellyn of Gwynedd in 1258, who was killed in battle by Edward I of England, and his brother David was executed. The Welsh princes demanded a new Prince of Wales who was born in the country and spoke the Welsh tongue from childhood. King Edward, whose young son Edward had been born in Caernarfon Castle and was still an infant, brought him before them and named him the new Prince of Wales. Prince Edward grew up speaking Welsh alongside French and English and so was invested with the title. From that point on, most English kings gave their eldest son and heir the Principality of Wales to govern before they became King of England. They didn't technically hold both titles at the same time, since they gave it up to their own son (if they had one) upon accession, however. But Edward II, Richard II, Henry V, Edward V and Henry VIII were all English kings who had been Princes of Wales prior to their accession (the title still existed post-Henry, but didn't carry any powers beyond a formality).
In 1337, Edward III of England lay claim to the throne of France (his mother had been the daughter of Philip IV), starting the Hundred Years War. His successor Henry V's military victories led to the proclaimation of his son Henry VI as a claimant King of France in 1422. This was the dispute between Henry and Charles VII, that led to Charles' victory and the end of the English claim to the French throne.
On the other side, there had been a French claim to the English throne through Louis VIII in 1215. Louis was married to Blanche, the niece of King John of England. John's war with the barons led to them inviting the French to invade and put Louis on the throne. Louis entered London and was proclaimed King in the summer of 1216, however, John's death that autumn caused the barons to switch to supporting his nine year old son Henry instead. Following Louis' defeat in battle, he agreed to leave the throne to Henry and quitted his claim.
In the same manner, William, Lord Protector (Stadtholder) of the Dutch Republic, was, as a grandson of Charles I, invited by the English nobles to depose his uncle James (Charles' son), and marry his cousin Mary as a joint-rulership of William III and Mary II.
Mary I of England was Queen of Spain by her marriage to Philip II, while Philip was named King of England and Ireland. However, they agreed largely not to interfere with one another's dominions. When Mary died, Philip lost his claim but did try and negotiate a marriage with her half-sister Elizabeth.
All Kings of England and Ireland (from James I until Anne) were also Kings of Scotland by virtue of being the same person, but the two kingdoms (England & Scotland) were governed seperately until 1707 with the formation of the United Kingdom of Great Britain. Ireland would be joined to them in 1800.
Malta was a British protectorate during the Napoleonic Wars and was made a Crown Colony in 1813 (under George III). This lasted until the establishment of first home rule and then the Republic of Malta in 1964.
Cyprus was made a protectorate under Queen Victoria in 1878 in exchange for support for the Ottomans against Russia. When the Ottomans joined the Central Powers in the First World War, Britain annexed the isle and declared it a Crown Colony under George V in 1925. Cyprus became an independent republic in 1959.