Most prominent members of the Rothschild family
I would like to start clarifying that by "bloodlines of the Illuminati", I am not referring to Weishaupt’s original order, but to those families that funded Weishaupt and who would later be also known as the “Illuminati”.
Mayer Amschel Rothschild successfully kept the fortune in the family through endogamy (with carefully arranged marriages between second and first cousins and other members of the family). He had 5 sons:
The first born was Amschel Mayer Rothschild, in 1773. On the death of his father in 1812, he succeeded as head of the bank at Frankfurt-am-Main (Germany), and died childless in 1855. 
The second was Salomon Mayer Rothschild, born in 1774. He was sent to Vienna (Austria) in 1820 to formalize the family's existing involvements in financing Austrian government projects. His bank, the S M von Rothschild, financed various government undertakings where large amounts of capital had to be raised. He made connections amongst the country's aristocracy and its political elite, and in recognition of his services he was made part of the Austrian nobility when awarded the hereditary title "Freiherr" (Baron) in 1822. In 1824 he married his own niece, the daughter of his brother Jacob. In 1843, he became the first Jew to ever be given honorary Austrian citizenship. Under his control the Viennese bank was highly successful, but the concentration of wealth in the hands of a few members of the elite resulted in a growing civil unrest in the country, a national anti-Rothschild sentiment, and ultimate in the involvement of Austria in the revolutions of 1848; after which Solomon left the business in the hands of his son, Anselm Salomon, and retired to Paris; where he died in 1855. 
The third born, in 1777, was Nathan Mayer Rothschild. In 1798 he was sent to England, and began to deal on the London stock exchange in financial instruments such as foreign bills of exchange and government securities. From 1811 he undertook the transfer of money to pay Wellington's troops (against Napoleon). Nathan’s four brothers helped to co-ordinate the activities across the continent, and the family developed a network of agents, shippers and couriers to transport gold and information across Europe. This private intelligence service enabled Nathan to receive in London the news of Wellington's victory at the Battle of Waterloo a full day ahead of the government's official messengers (which he allegedly used to deceive other investors in the London Stock Exchange, making him a fortune; though Rothschild researchers, and others, deny these allegations). In 1818 he arranged a £5 million loan to the Prussian government and the issuing of bonds for government loans formed a mainstay of his bank’s business. He gained a position of such power in the City of London that by 1825/6 that he was able to supply coins to the Bank of England. He was also known for his role in the abolition of the slave trade; however, records from the National Archives examined in 2009 show that Nathan financially benefited from slavery. In 1869, his grandson became a director of the Bank of England, a post he held for 20 years. The Rothschild bank also funded Cecil Rhodes in the development of the British South Africa Company and the Rothschild family administered Rhodes's estate after his death in 1902, and helped to set up the Rhodes Scholarship scheme  (which many presidents, UN key figures, politicians and government officials worldwide would receive). 
The fourth born was Calmann Mayer Rothschild, in 1788. The 1821 occupation of Naples by the Austrian army provided the opportunity for Calmann (Carl) to set up his business in the Kingdom. As such, Carl was sent to Naples where he established C M de Rothschild & Figli to operate as a satellite office to the Rothschild banking family in Germany. He established a good working relationship with Luigi de' Medici, the "Direttore della Segreteria di Azienda del Regno di Napoli" (Finance Minister), and his operation became the dominant banking house in Naples. In 1829, Carl was appointed consul-general of Sicily at Frankfurt and in January 1832 the Jewish banker was given a ribbon and star of the Sacred Military Constantinian Order of Saint George at a ceremony with the new Roman Catholic Pope, Gregory XVI. 
Jacob (James) Mayer Rothschild was the last born in 1792, but I've already explained his success in Paris in the previous chapter. However, it’s worth mentioning that many Rothschilds were, and are, supporters of the State of Israel, although others oppose it. Either way, James' grandson, Edmond Benjamin James de Rothschild, was a strong supporter of Zionism, and his generous donations lent significant support to the movement during its early years which helped lead to the establishment of the State of Israel.  He was also a patron of the first settlement in Palestine at Rishon-LeZion, and bought from Ottoman landlords many parts of the land which now makes up present-day Israel. In 1917 Walter Rothschild was the addressee of the Balfour Declaration, which committed the British government to the establishment in Palestine of a national home for the Jewish people. James A. de Rothschild financed the Knesset building as a gift to the State of Israel. The Supreme Court of Israel building was donated to Israel by Dorothy de Rothschild;  Outside the President's Chamber is displayed the letter Mrs Rothschild wrote to Prime Minister Shimon Peres expressing her intention to donate a new building for the Supreme Court. 
After amassing huge fortunes, the name Rothschild became synonymous with extravagance and great wealth. By the end of the century, the family owned, or had built, at the lowest estimates, over 41 palaces, of a scale and luxury perhaps unparalleled even by the richest Royal families.  The British Prime Minister Lloyd George claimed, in 1909, that Lord Nathan Rothschild was the most powerful man in Britain.  The business magazine referred to Mayer Amschel Rothschild as the "founding father of international finance", and Forbes magazines as the “20th most influential businessmen of all times". 
From the mid 19th century, many people had their eyes on the Rothschilds and their activities. Suspicion and an anti-Rothschild sentiment spread throughout Europe. It was time to keep a low public profile and to put in place a network of frontmen to take care of their businesses. By the later 19th century, almost all Rothschilds had started to marry outside the family, usually into the aristocracy or other financial dynasties, like the: Warburg, Oppenheim, House of Bonaparte, Wellington, Guinness, House of Borghese, Ephrussi, Walpole, Wodehouse, and many others.
… Next chapter: the conquest of the New World
Wikipedia: Rothschild family (http://en.wikipedia.org/wiki/Rothschild_family)
 Wikipedia: Amschel Mayer Rothschild (http://en.wikipedia.org/wiki/Amschel_Mayer_Rothschild)
 Wikipedia: Solomon Mayer Rothschild (http://en.wikipedia.org/wiki/Salomon...von_Rothschild)
 Wikipedia: Nathan Mayer Rothschild (http://en.wikipedia.org/wiki/Nathan_Mayer_Rothschild)
 Wikipedia: List of Rhodes Scholars (http://en.wikipedia.org/wiki/List_of_Rhodes_Scholars)
 Wikipedia: Carl Mayer von Rothschild (http://en.wikipedia.org/wiki/Carl_Mayer_von_Rothschild)
 Wikipedia: Edmond James de Rothschild (http://en.wikipedia.org/wiki/Edmond_James_de_Rothschild)
 The New York Times, "Dorothy de Rothschild, 93, Supporter of Israel" (obituary), 13 December 1988.
 The Presidents Chamber, Tour of Supreme Court, The Judicial Authority. http://elyon1.court.gov.il/eng/home/index.html
 Niall Ferguson, "The Ascent of Money: A Financial History of the World", London 2008, page 78.
 Paul Johnson, "A History of the Jews ", London 2004, page 319-20