Noble gases is one of the most common designations for the Elements in the rightmost group of the periodic table of the elements, they are also sometimes called 'inert gases'. For a number of complicated reasons, these elements have one important chemical property: they are extremely un-reactive. One consequence of this was that the noble gases were isolated and characterised only relatively late.
The first person to actually isolate and note the presence of these noble gases - however without going into further details - was Henry Cavendish (1731-1810 chemistry big-one and discoverer of hydrogen) in 1785. He removed all the nitrogen and oxygen chemically from a receptacle contining air. The nitrogen was oxidised to NO2 by electric discharges and absorbed by a sodium hydroxide solution. Remaining oxygen was removed from the mixture by a special adsorber. 1/120 of the gas volume remained unreacted in the receptacle. As we know today, this must have been mainly argon (99.8%) and traces (0.2%) of other noble gases. The second person to isolate a noble gas, but without characterising it, was mineralogist William Francis Hillebrand (1853-1925) who noted the formation of a gas while dissolving uranium containing minerals in acid. We know today this must have been helium.
In 1894 John William Strutt, third Baron Rayleigh, (1842-1919) noted that 'pure' Nitrogen isolated from air was denser than pure nitrogen obtained chemically (1.2567 g/l against 1.2505 g/l at 0°C and 1.013 bar). From that he concluded that something else was in the air. Together with physico-chemist Wiliam Ramsay (1852-1916) they decided to take a closer look at that un-reactive fraction of air Cavendish had noticed earlier. While Rayleigh repeated Cavendish's experiment Ramsay modified it a bit: the oxygen was removed by reacting it with heated copper (copper reacts with oxygen to cuprous oxide) and the nitrogen was removed by reacting it with magnesium (magnesium reacts with nitrogen to form magnesium nitride). The remaining fraction was then properly characterised. The new element was called 'argon' which comes from the Greek word for 'inert'.
One year later, in 1895, Ramsay and - independently - Per Theodor Cleve (1840-1905) isolated and characterized that gas, which had been discovered by Hillebrand. Its spectral lines coincided with many lines observed in the sun's spectrum, about thirty years earlier, in 1868. In fact the existence of this element had been postulated by the astronomers Pierre Jules Cesar Jansen (1824-1907) and - independently - Sir Joseph Norman Lockyer (1836-1920), who named it helium (from the Greek word for 'sun').
Neon, Krypton and Xenon
After the development of the periodic table of elements in the 1870s and the discovery of argon and helium, Ramsay realized there were even more spaces left blank in that table for undiscovered elements, which should all be 'noble gases'. He wouldn't have gotten far in his search for those new 'noble gases' were it not it for the invention of air liquefaction by Carl von Linde. Ramsay had one of Linde's machines re-built in his lab (the original Machine can be seen here: Deutsches Museum: Linde's Air Liquefaction Machine) and obtained litres and litres of noble gas mixtures (the left-over from the liquefaction). In 1898 Ramsay 'distilled' the left over and found not only neon (which obtained this name from the greek word for 'new'), which was the element he was looking for, but also krypton (greek for 'hidden') and xenon (greek for 'strange').
The last noble gas to be isolated was radon, in 1900, by Friedrich Ernst Dorn (1848-1916). Another isotope of radon had been observed earlier in 1899 by Ernest Rutherford (1871-1937) and Frederick Soddy (1877-1956). While the discussions were going on about who really isolated that element first, people found out that radon has been observed even earlier, by the Curies (Marie and Pierre) because it is a gaseous product of the radioactive decay of radium, so there was always a 'strange' gas bubble in sealed ampoules containing radium or uranium solutions. It was originally called 'niton' (from the latin word 'nitens' which means 'shining'). The gas was properly characterised by - you guessed it - Ramsay in 1908, who found out that the gas is a heavy, colourless and odourless noble gas. It was finally called 'radon' because the most stable isotope emanates from radium solutions. (Radon emanating from actinium solutions was called actinon, and radon emanating from thorium solutions used to be called thoron).
What happened to all those folks?
Henry Cavendish was what we would call today a strange scientist 1, also he was shy and afraid of women. A bio of this eccentric scientist can be found here on BBC: Historic Figures: Henry Cavendish. William Francis Hillebrand achieved some fame as one of the greatest analytical chemists and mineralogists of his time. Rayleigh and Ramsay went Nobel in 1904, in physics and chemistry, respectively. Rayleigh "for his investigations of the densities of the most important gases and for his discovery of argon in connection with these studies". And for Ramsay "in recognition of his services in the discovery of the inert gaseous elements in air, and his determination of their place in the periodic system". Per Theodor Cleve (1840-1905) had the mineral formed by uranium dioxide named after him: Cleveite. Joseph Norman Lockyer (1836-1920), who, along with Pierre Jansen, was the first to see the spectrum of helium, was knighted just right after Ramsay isolated helium and confirmed the existence of that element. Lockyer was also the founder of Nature one of the most renowned scientific Journals. The other astronomer, Pierre Jules Cesar Jansen (1824-1907), later specialized in solar photography. His work in this field - published in 1904 - set the standard for almost 50 years. The German physicist Friedrich Ernst Dorn (1848-1916), who was one of the discoverers of radon, became the director of the physical institute of Halle, Germany. Ernest Rutherford (1871-1937) ended up getting his place in the list of Nobel laureates in 1908, "for his investigations into the disintegration of the elements, and the chemistry of radioactive substances" - including Radon. The Curies (Marie and Pierre) were awarded a half Nobel Prize in Physics in 1903 More detailed bios of the Nobel people can be found here: nobel.se.
Recent Noble Gas History
Soon after the discovery of the noble gases people started to ask why (and if) these elements are (really) inert. At the same time there was quite a turmoil going on around the quantum theory. In the end people figured out all things about electrons moving around atoms and how it comes that certain compounds form and some don't. The explanation behind the noble gas' 'inertness' was that their electronics was the most stable configuration possible in the first place, so building a compound would only make them less stable. In fact, it was even postulated, that noble gases can't form a compound. In 1933 Pauling rose serious doubts whether that is absolutely true. He figured out that it should be - in principle - possible to obtain noble gas compounds, well, at least of the heavier gases krypton and xenon. He proposed low reactivity instead of no reactivity for the noble gases. The final proof for Linus' case came in 1962 - quite as a surprise, by the way - when British scientist Neil Bartlett was messing around with a very tough oxidizer (platinum hexafluoride) and xenon. He ended up obtaining a yellow solid compound (xenon hexaflouroplatinate2). This first synthesis of a noble gas compound ignited a noble-gas-compound frenzy, and soon many other compounds were synthesised. At the date of writing only neon and helium, the two lightest noble gases, were not found to form chemical compounds. However, chemists are developing strategies to bind even these elements.