
Australia
1. Piano, The [Campion, Jane; 1993] #81 - Australia
2. Shine [Hicks, Scott; 1996] #574 - Australia
3. Mad Max 2, aka Road Warrior [Miller, George; 1981] #590 - Australia
4. Walkabout [Roeg, Nicolas; 1971] #672 - Australia
5. Picnic at Hanging Rock [Weir, Peter; 1975] #730 – Australia
6. An Angel at My Table, An [Campion, Jane; 1990] #737 - New Zealand-Aust-UK
7. Forbidden Lie$ [Broinowski, Anna; 2007] #1028 - Australia
8. Year of Living Dangerously, The [Weir, Peter; 1982] #1136 - Australia
9. Moulin Rouge! [Luhrmann, Baz; 2001] #1184 - Australia-US
[see bottom of this post for a list of Australian Film Institute awards for best picture]

Babe (Chris Noonan, 1995) [This won 17 international awards, nominated for Best Picture, how can it not make any film polls? Produced by Road Warrior director George Miller]
My Brilliant Career (Gillian Armstrong, 1979) - energetic romantic adventure
Breaker Morant (Bruce Beresford, 1980) - terrific war story based on fact
The Proposition (John Hillcoat, 2005) – a gutsy western
The Last Wave (Peter Weir, 1977) - aboriginal folk tale of the apocalypse
Flirting (John Duigan, 1980) - insightful interracial love story, Nicole Kidman co-stars
The Man From Snowy River (George Miller, 1982) – not the same George Miller as above (this one's from Scotland), another Aussie western
Australia (Baz Luhrmann, 2008) - enjoyable epic western romance, with some war thrown in as well
My own favorite Aussie films are: Babe, Walkabout, The Road Warrior (a classic in mayhem), My Brilliant Career, Picnic at Hanging Rock, Flirting, The Piano, The Proposition, Shine, The Man From Snowy River
Update: add Animal Kingdom (2010)
New Zealand
1. Lord of the Rings: The Fellowship of the Ring [Jackson, Peter; 2001] #84 - US-New Zealand
2. Lord of the Rings: The Return of the King [Jackson, Peter; 2003] #97 - US-New Zealand
3. Lord of the Rings: The Two Towers [Jackson, Peter; 2002] #144 - US-New Zealand
4. An Angel at My Table [Campion, Jane; 1990] #737 - New Zealand
Canada
1. Wavelength [Snow, Michael; 1967] #263 - Canada
2. Sweet Hereafter, The [Egoyan, Atom; 1997] #319 - Canada
3. Dead Ringers [Cronenberg, David; 1988] #355 - Canada
4. Atlantic City [Malle, Louis; 1980] #491 - Canada-France
5. Fast Runner, The [Kunuk, Zacharias; 2001] #620 - Canada
6. Videodrome [Cronenberg, David; 1983] #705 - Canada
7. Hart of London, The [Chambers, Jack; 1970] #711 - Canada
8. Région centrale, La [Snow, Michael; 1971] #725 - Canada*
9. Capote [Miller, Bennett; 2005] #760 - Canada-US
10. Away from Her [Polley, Sarah; 2006] #774 - Canada
11. Crash [Cronenberg, David; 1996] #984 - Canada
12. My Winnipeg [Maddin, Guy; 2007] #1096 - Canada
13. Barbarian Invasions, The [Arcand, Denys; 2003] #1207 - Canada*
* = in French, with subtitles
I think the last of these, foreign language Oscar® winner Barbarian Invasions, about a man dying of cancer with his family and friends around to send him off, is my favorite Canadian film (in French, with subtitles).
However, The Sweet Hereafter (in English) is a minor masterpiece, imo, which also deals with death, as lawyer Ian Holm shows up in a small Canadian town to try to get them to seek justice after a fatal school bus accident.
Atlantic City, with Burt Lancaster and Susan Sarandon, is Louis Malle's best to me, though it really feels like US film, another crime/noir story.
Apparently, Wavelength is an experimental film designed to get people to leave the theater with noise, I don't know how it out-polled the more serious films.
Australian Film Institute Awards for Best Picture [only films produced in Australia]
2008 - The Black Balloon
2007 - Romulus, My Father
2006 - Ten Canoes
2005 - Look Both Ways
2004 - Somersault
2003 - Japanese Story
2002 - Rabbit-Proof Fence
2001 - Lantana
2000 - Looking for Alibrandi
1999 - Two Hands
1998 - The Interview
1997 - Kiss or Kill
1996 - Shine
1995 - Angel Baby
1994 - Muriel's Wedding
1993 - The Piano
1992 - Strictly Ballroom
1991 - Proof
1990 - Flirting
1989 - Evil Angels (aka. A Cry in the Dark)
1988 - The Navigator: A Medieval Odyssey
1987 - The Year My Voice Broke
1986 - Malcolm
1985 - Bliss
1984 - Annie's Coming Out
1983 - Careful, He Might Hear You
1982 - Lonely Hearts
1981 - Gallipoli
1980 - Breaker Morant
1979 - My Brilliant Career
1978 - Newsfront
1977 - Storm Boy
1976 - The Devil's Playground
1974/5 - Sunday Too Far Away
1973 - Libido: The Child
1973 - 27A
1972 - Stork
1971 - Homesdale
1970 - Three To Go: Michael
1969 - Jack And Jill: A Postscript
1968 - The Change at Groote / The Talgai Skull
1967 - Cardin in Australia
1966 - Concerto for Orchestra
1965 - The Legend of Damien Parer / Stronger Since The War
1964 - The Dancing Class / I The Aboriginal
1963 - The Land That Waited
1962 - Bypass to Life / Night Freighter
1961 - Not awarded this year
1960 - Three in a Million
1959 - Edge of The Deep / The Power Makers
1958 - Conquest of The Rivers / Hard to Windward