Here are the 96 Nobel Prizewinners who attended Cambridge University that I have found during my research. For more information on any of the Laureates, see the Nobel Archive

Laureate	College	Prize	Year	Reason for Prize
Lord Rayleigh	Trinity	Phy	1904	Discovered Argon
JJ Thomson	Trinity	Phy	1906	Investigated the electrical conductivity of gases
Ernest Rutherford	Trinity	Che	1908	Atomic structure and radioactivity
William Bragg	Trinity	Phy	1915	Analysed crystal structure using X-rays
Lawrence Bragg	Trinity	Phy	1915	Analysed crystal structure using X-rays
Charles Barkla	Trinity	Phy	1917	Discovered the characteristics of X-radiation
Niels Bohr	Trinity	Phy	1922	Investigated atomic structure and radiation
Francis Aston	Trinity	Che	1922	Work on mass spectroscopy and the `whole number rule'
Archibald Hill	Trinity	Med	1922	Heat production in the muscles
Austen Chamberlain	Trinity	Pea	1925	Work on the Locarno Pact, 1925
Charles Wilson	Sidney Sussex	Phy	1927	Invented the cloud chamber
Arthur Holly Compton	-	Phy	1927	Discovered wavelength change in diffused X-rays
Owen Richardson	Trinity	Phy	1928	Richardson's Law of electron emission of hot metals
Frederick Hopkins	Trinity/ Emmanuel	Med	1929	Discovered growth stimulating vitamins
Lord Adrian	Trinity	Med	1932	The function of neurons
Charles Sherrington	Caius	Med	1932	The function of neurons
Paul Dirac	St John's	Phy	1933	Quantum mechanics
James Chadwick	Caius	Phy	1935	Discovered the neutron
Henry Dale	Trinity	Med	1936	The chemical transmission of nerve impulses
George Thomson	Trinity	Phy	1937	Interference in crystals irradiated by electrons
Albert Szent-Gyorgyi	Fitzwilliam	Med	1937	Combustion in biology
Ernst Chain	Fitzwilliam	Med	1945	Discovery of penicillin
Howard Florey	Caius	Med	1945	Discovery of penicillin
Edward Appleton	St John's	Phy	1947	Discovered the Appleton Layer
Patrick Blackett	Magdalene/ King's	Phy	1948	Nuclear physics and cosmic radiation
Bertrand Russell	Trinity	Lit	1950	A History of Western Philosophy, 1945
Cecil Powell	Sidney Sussex	Phy	1950	Photography of nuclear processes
John Cockcroft	St John's/ Churchill	Phy	1951	Used accelerated particles to study atomic nuclei
Ernest Walton	Trinity	Phy	1951	Used accelerated particles to study atomic nuclei
Richard Synge	Trinity	Che	1952	Developed partition chromatography
Archer Martin	Peterhouse	Che	1952	Developed partition chromatography
Hans Krebs	-	Med	1953	Discovered the citric acid cycle
Max Born	-	Phy	1954	Fundamental research into quantum mechanics
Alexander Todd	Christs	Che	1957	Work on nucleotides
Frederick Sanger	St John's	Che	1958	Structure of the insulin molecule
Philip Noel-Baker	King's	Pea	1959	Work towards global disarmament
John Kendrew	Trinity	Che	1962	Determined the structure of haemoproteins
Max Perutz	Peterhouse	Che	1962	Determined the structure of haemoproteins
Francis Crick	Caius/ Churchill	Med	1962	Structure of DNA
James Watson	Clare	Med	1962	Structure of DNA
Maurice Wilkins	St John's	Med	1962	Structure of DNA
Alan Hodgkin	Trinity	Med	1963	Transmission of nerve impulses along a nerve fibre
Andrew Huxley	Trinity	Med	1963	Transmission of nerve impulses along a nerve fibre
Dorothy Hodgkin	Newnham/ Girton	Che	1964	Structure of compounds used in fighting anaemia
Ronald Norrish	Emmanuel	Che	1967	Study of fast chemical reactions
George Porter	Emmanuel	Che	1967	Study of fast chemical reactions
Rodney Porter	Pembroke	Med	1972	Chemical structure of antibodies
John Hicks	Caius	Eco	1972	Equilibrium theory
Brian Josephson	Trinity	Phy	1973	Tunneling in superconductors and semiconductors
Patrick White	King's	Lit	1973	For an epic and psychological narrative art which has introduced a new continent into literature
Martin Ryle	Trinity	Phy	1974	For the invention of aperture synthesis
Antony Hewish	Caius/ Churchill	Phy	1974	For the discovery of pulsars
Nevill Mott	Caius/ St John's	Phy	1977	Behaviour of electrons in magnetic solids
Philip Anderson	Churchill	Phy	1977	Behaviour of electrons in magnetic solids
James Meade	Trinity	Eco	1977	Contributed to the theory of international trade
Pyotr Kapitsa	Trinity	Phy	1978	Invented the helium liquefier
Peter Mitchell	Jesus	Che	1978	Energy transfer processes in biological systems
Abdus Salam	St John's	Phy	1979	Unification of electromagnetic and weak particle interactions
Steven Weinberg	-	Phy	1979	Unification of electromagnetic and weak particle interactions
Allan Cormack	St John's	Med	1979	Development of CAT scans
Walter Gilbert	Trinity	Che	1980	Developed the theory of nucleotide links in nucleic acids
Frederick Sanger	St John's	Che	1980	Developed the theory of nucleotide links in nucleic acids
Aaron Klug	Trinity	Che	1982	Determined the structure of biologically active substances
Subrahmanyan Chandrasekhar	Trinity	Phy	1983	The evolution and devolution of stars
William Fowler	Pembroke	Phy	1983	The evolution and devolution of stars
Gerard Debreu	Churchill	Eco	1983	Reformulation of the theory of general equilibrium
Richard Stone	Caius	Eco	1984	Developing a national income accounting system
Cesar Milstein	Fitzwilliam	Med	1984	Developed a technique for producing monoclonal antibodies
Georges Kohler	-	Med	1984	Developed a technique for producing monoclonal antibodies
Norman Ramsey	Clare	Phy	1989	Developing the separated field method
James Mirrlees	Trinity	Eco	1996	Studied behaviour in the absence of complete information
John Walker	Sidney Sussex	Che	1997	Studied how a spinning enzyme creates the molecule that powers cells in muscles
Amartya Sen	Trinity	Eco	1998	For his contributions to welfare economics
John Pople	Trinity	Che	1998	For his development of computational methods in quantum chemistry
Alan McDiarmid	Sidney Sussex	Che	2000	For the discovery and development of conductive polymers
Paul Greengard	?	Med	2000	For discoveries concerning signal transduction in the nervous system
Tim Hunt	Clare	Med	2001	For discoveries of key regulators of the cell cycle
Joseph Stiglitz	Caius	Eco	2001	For analyses of markets with asymmetric information
John Sulston	Pembroke	Med	2002	For discoveries concerning genetic regulation of organ development and programmed cell death
Sydney Brenner	King's	Med	2002	For discoveries concerning genetic regulation of organ development and programmed cell death
Richard Schrock	-	Che	2005	For the development of the metathesis method in organic synthesis
Martin Evans	Christ's	Med	2007	For discoveries of principles for introducing specific gene modifications in mice
Roger Tsien	Churchill	Che	2008	For increasing understanding of the protein GFP
Elizabeth Blackburn	Darwin	Med	2009	For the discovery of how chromosomes are protected by telomeres and the enzyme telomerase
Venkatraman Ramakrishnan	Trinity	Che	2009	For studies of the structure and function of the ribosome
Robert Edwards	Churchill	Med	2010	For the development of in vitro fertilization
John Gurdon	Churchill/ Magdalene	Med	2012	For the discovery that mature cells can be reprogrammed to become pluripotent
Michael Levitt	Peterhouse	Che	2013	For the development of multiscale models for complex chemical systems
Angus Deaton	Fitzwilliam	Eco	2015	For his analysis of consumption, poverty, and welfare
Oliver Hart	King's	Eco	2016	For his contributions to contract theory
John Kosterlitz	Caius	Phy	2016	For theoretical discoveries of topological phase transitions and topological phases of matter
Duncan Haldane	Christ's	Phy	2016	For theoretical discoveries of topological phase transitions and topological phases of matter
David Thouless	Trinity Hall	Phy	2016	For theoretical discoveries of topological phase transitions and topological phases of matter
Richard Henderson	Corpus Christi	Che	2017	For developing cryo-electron microscopy for the high-resolution structure determination of biomolecules in solution
Peter Ratcliffe	Caius	Med	2019	For discoveries of how cells sense and adapt to oxygen availability
Didier Queloz	Trinity	Phy	2019	For work on exoplanets and the evolution of the Universe

Thanks to Martin Boer, and the University Press and Publications office for finding several that I had missed, and to Edward Hoffman for many of the links below.

Chicago (85 Nobelists), MIT (73), Columbia (72), Harvard (>43), Oxford (48), Gottingen (44), Cornell (40), Princeton (32), John Hopkins (32), Caltech (31), Humboldt, Berlin (29), Stanford (23), Manchester (23), Washington Uni. St Louis (21), Rockefeller (21), Berkeley (20), Yale (18), Illinois (Urbana-Champaign) (18), Pennsylvania (16), Imperial College, London (14), LSE (14), and Liverpool (8), maintain their own impressive lists of Nobel Prizewinning alumni, but their criteria for deciding who is an alumnus vary wildly, and are on the whole different to those here. If only Undergraduate and Graduate Students are counted as having studied at an institution then these totals drop to perhaps 37 for Columbia and 29 for Chicago (compared to up to 48 for Harvard). By the same criteria, Cambridge loses Compton, Hicks, Fowler, Walker, Debreu, Kohler, Greengard, Weinberg, Brenner, Stiglitz, Ramakrishnan, Gurdon and Queloz leaving 83 who were actually students here.

Wikipedia has a detailed if inconsistent page on the alma maters of Nobel Prizewinners. See also here for a further list of links to Nobel Prizewinning Alumni pages.