Raph's got a list of all the Hugo winners and is way beyond the number I've read - but I wonder if I could Mooch my way through the rest...

(bold = read, italics = I think I read)

2006 Spin, Robert Charles Wilson
2005 Jonathan Strange & Mr Norrell, Susanna Clarke (half-read - gave up and sent on to a Moocher)
2004 Paladin of Souls, Lois McMaster Bujold
2003 Hominids, Robert J. Sawyer
2002 American Gods, Neil Gaiman
2001 Harry Potter and the Goblet of Fire, J. K. Rowling (how'd this win...)
2000 A Deepness in the Sky, Vernor Vinge
1999 To Say Nothing of the Dog, Connie Willis
1998 Forever Peace, Joe Haldeman
1997 Blue Mars, Kim Stanley Robinson
1996 The Diamond Age, Neal Stephenson
1995 Mirror Dance, Lois McMaster Bujold
1994 Green Mars, Kim Stanley Robinson
1993 Doomsday Book, Connie Willis
1993 A Fire Upon the Deep, Vernor Vinge
1992 Barrayar, Lois McMaster Bujold
1991 The Vor Game, Lois McMaster Bujold
1990 Hyperion, Dan Simmons
1989 Cyteen, C. J. Cherryh
1988 The Uplift War, David Brin (mooched)
1987 Speaker for the Dead, Orson Scott Card
1986 Ender’s Game, Orson Scott Card
1985 Neuromancer, William Gibson (mooched)
1984 Startide Rising, David Brin (mooched)
1983 Foundation’s Edge, Isaac Asimov (mooched)
1982 Downbelow Station, C. J. Cherryh (mooched)
1981 The Snow Queen, Joan D. Vinge (mooched)
1980 The Fountains of Paradise, Arthur C. Clarke (mooched)
1979 Dreamsnake, Vonda N. McIntyre (amazoned)
1978 Gateway, Frederik Pohl (mooched - pending)
1977 Where Late the Sweet Birds Sang, Kate Wilhelm (amazoned)
1976 The Forever War, Joe Haldeman (amazoned)
1975 The Dispossessed, Ursula K. Le Guin (amazoned)
1974 Rendezvous with Rama, Arthur C. Clarke (mooched)
1973 The Gods Themselves, Isaac Asimov (mooched)
1972 To Your Scattered Bodies Go, Philip José Farmer (mooched)
1971 Ringworld, Larry Niven (mooched)
1970 The Left Hand of Darkness, Ursula K. Le Guin (mooched)
1969 Stand on Zanzibar, John Brunner (amazoned)
1968 Lord of Light, Roger Zelazny (amazoned, but stolen?)
1967 The Moon Is a Harsh Mistress, Robert A. Heinlein (amazoned)
1966 Dune, Frank Herbert (amazoned)
1966 “…And Call Me Conrad” (This Immortal), Roger Zelazny (amazoned)
1965 The Wanderer, Fritz Leiber (amazoned)
1964 “Here Gather the Stars” (Way Station), Clifford D. Simak (moochable, but from Oz - and available for 99p on Amazon)
1963 The Man in the High Castle, Philip K. Dick (mooched)
1962 Stranger in a Strange Land, Robert A. Heinlein (mooched)
1961 A Canticle for Leibowitz, Walter M., Miller Jr (refused mooch, bought from Amazon)
1960 Starship Troopers, Robert A. Heinlein (mooched)
1959 A Case of Conscience, James Blish (mooched)
1958 The Big Time, Fritz Leiber (unmoochable, bought via Amazon from the Book Bothy)
1956 Double Star, Robert A. Heinlein (mooched, reviewed)
1955 They’d Rather Be Right (The Forever Machine), Mark Clifton & Frank Riley (unmoochable, bought 2nd hand; reviewed)
1953 The Demolished Man, Alfred Bester (mooched; reviewed)