Section 51 (xxxv) - conciliation and arbitration for the prevention and settlement of industrial disputes extending beyond the limits of any one State - Amalgamated Society of Engineers v Adelaide Steamship Co Ltd ("Engineers' Case") (1920) 28 CLR 129,  HCA 54 - this case overturned the doctrine of implied intergovernmental immunities and reserved state powers and established the modern basis for the legal understanding of federalism in Australia.
Section 51 (xxxi) the acquisition of property on just terms from any State or person for any purpose in respect of which the Parliament has power to make laws - Newcrest Mining (WA) Ltd v Commonwealth (1997) 190 CLR 513,  HCA 38 - this case decided that when acquiring property in a Territory or in a State, the Commonwealth must do so on 'just terms'. In other words the majority in this case held that the Commonwealth had infringed section 51 (xxxi).
Mabo and Others v Queensland (No. 2) ("Mabo Case") (1992) 175 CLR 1,  HCA 23 - this decision recognised native title in Australia for the first time. The High Court rejected the doctrine of terra nullius in favour of the common law doctrine of aboriginal title.
Section 51 (xxix) external affairs - Commonwealth v Tasmania ("Tasmanian Dam Case") (1983) 158 CLR 1,  HCA 21 - in this case, the Commonwealth succeeded in stopping the building of a hydro-electricity dam proposed for Tasmania. It was held that the Commonwealth had power under section 51 (xxix) of the Constitution to stop the dam based on Australia's international obligations under the World Heritage Convention.
Section 51 (xxxix) - matters incidental to the execution of any power vested by this Constitution in the Parliament or in either House thereof, or in the Government of the Commonwealth, or in the Federal Judicature, or in any department or officer of the Commonwealth - Pape v Commissioner of Taxation (2009) 238 CLR 1,  HCA 23 - this case revolved around the constitutional validity of the Tax Bonus for Working Australians Act (No 2) 2009 (Cth) which gave one-off payments of up to $900 to Australian taxpayers. By a margin of 4-3, the High Court held that the Act was a valid law under the Constitution.
Section 51 (xxvi) - the people of any race
, other than the aboriginal race in any State, for whom it is deemed necessary to make special laws - Kartinyeri v Commonwealth (Hindmarsh Island Bridge Case) (1998) 195 CLR 337,  HCA 22 - dispute regarding the Hindmarsh Island Bridge and the issue regarding the scope of the race power. Click here for You Tube video.
In 1942, the Commonwealth passed four new laws designed to raise funds to support the war effort by encouraging the States to give up their right to collect income tax. On June 22 1942, South Australia, Victoria, Queensland and Western Australia went to the High Court seeking the legislation to be declared invalid. In the case of South Australia v Commonwealth (1942) (the First Uniform Tax Case) (1942) 65 CLR 373,  HCA 14, the High Court ruled that the four pieces of legislation were valid. In 1957, Victoria again challenged the constitutionality of the scheme. But in Victoria v Commonwealth (1957) (the Second Uniform Tax Case) (1957) 99 CLR 575,  HCA 54, the Court held that Commonwealth grants to the States under section 96 of the Constitution may be validly tied to prescribed purposes.
Section 51 (xxxi) the acquisition of property on just terms from any State or person for any purpose in respect of which the Parliament has power to make laws - Bank of New South Wales v The Commonwealth (1948) 76 CLR 1,  HCA 7, also known as the Bank Nationalisation Case, revolved around the Labor Government's attempt to nationalise private banks in Australia. The constitutional validity of the legislation was challenged and found to be invalid on two bases. The first of these was based upon an 'individual rights' interpretation of the operation of the constitutional freedom of interstate trade and commerce (s 92), which the Court held conferred a positive right on the banks to engage in the business of interstate banking. The second basis was that the mechanism used to nationalise the banks was not on "just terms" and therefore was outside the scope of section 51 (xxxi)
The Communist Party Case - Australian Communist Party v The Commonwealth (1951) 83 CLR 1,  HCA 5 - this case revolved around the validity of the Communist Party Dissolution Act introduced by Prime Minister Menzies in 1950 pledging to dissolve the Australian Communist Party. The justices held that the Commonwealth had legislative power to protect itself from subversion under the Crimes Act 1914 (Cth) yet the Communist Party Dissolution Act had simply declared the party guilty in its 'recitals' in the preamble and was therefore invalid.
R v Kirby; Ex parte Boilermakers' Society of Australia ("Boilermakers Case ") (1956) 94 CLR 254 ,  HCA 10 - the Boilermakers Case was an important separation of powers case in Australia. The majority of the High Court applied the separation doctrine to find that the Commonwelath Court of Conciliation and Arbitration could not validly exercise judicial functions. As a result, the Conciliation and Arbitration Act 1904 was amended to establish two separate bodies.
Cole v Whitfield (1988) 165 CLR 360,  HCA 18 - in this case, the High Court overruled the long-held notion that the words "absolutely free" in section 92 of the Australian Constitution protected a personal individual right of freedom in interstate trade. It was instead replaced with the economic notion of "free trade".
Source: Australian Constitutional Landmarks edited by H.P. Lee and George Winterton (Cambridge, 2003)