After a week or two of seeing this I decided to bite the bullet and do it. Here it is, NPR's "Top 100 Science Fiction Novels", with the ones I've read in bold. (30/100; acceptable I suppose.)
1. The Lord Of The Rings Trilogy, by J.R.R. Tolkien
2. The Hitchhiker's Guide To The Galaxy, by Douglas Adams
3. Ender's Game, by Orson Scott Card
4. The Dune Chronicles, by Frank Herbert
5. A Song Of Ice And Fire Series, by George R. R. Martin
6. 1984, by George Orwell
7. Fahrenheit 451, by Ray Bradbury
8. The Foundation Trilogy, by Isaac Asimov
9. Brave New World, by Aldous Huxley
10. American Gods, by Neil Gaiman
11. The Princess Bride, by William Goldman
12. The Wheel Of Time Series, by Robert Jordan
13. Animal Farm, by George Orwell
14. Neuromancer, by William Gibson
15. Watchmen, by Alan Moore
16. I, Robot, by Isaac Asimov
17. Stranger In A Strange Land, by Robert Heinlein
18. The Kingkiller Chronicles, by Patrick Rothfuss
19. Slaughterhouse-Five, by Kurt Vonnegut
20. Frankenstein, by Mary Shelley
21. Do Androids Dream Of Electric Sheep?, by Philip K. Dick
22. The Handmaid's Tale, by Margaret Atwood
23. The Dark Tower Series, by Stephen King
24. 2001: A Space Odyssey, by Arthur C. Clarke
25. The Stand, by Stephen King
26. Snow Crash, by Neal Stephenson
27. The Martian Chronicles, by Ray Bradbury
28. Cat's Cradle, by Kurt Vonnegut
29. The Sandman Series, by Neil Gaiman
30. A Clockwork Orange, by Anthony Burgess
31. Starship Troopers, by Robert Heinlein
32. Watership Down, by Richard Adams
33. Dragonflight, by Anne McCaffrey
34. The Moon Is A Harsh Mistress, by Robert Heinlein
35. A Canticle For Leibowitz, by Walter M. Miller
36. The Time Machine, by H.G. Wells
37. 20,000 Leagues Under The Sea, by Jules Verne
38. Flowers For Algernon, by Daniel Keys
39. The War Of The Worlds, by H.G. Wells
40. The Chronicles Of Amber, by Roger Zelazny
41. The Belgariad, by David Eddings
42. The Mists Of Avalon, by Marion Zimmer Bradley
43. The Mistborn Series, by Brandon Sanderson
44. Ringworld, by Larry Niven
45. The Left Hand Of Darkness, by Ursula K. LeGuin
46. The Silmarillion, by J.R.R. Tolkien
47. The Once And Future King, by T.H. White
48. Neverwhere, by Neil Gaiman
49. Childhood's End, by Arthur C. Clarke
50. Contact, by Carl Sagan
51. The Hyperion Cantos, by Dan Simmons
52. Stardust, by Neil Gaiman
53. Cryptonomicon, by Neal Stephenson
54. World War Z, by Max Brooks
55. The Last Unicorn, by Peter S. Beagle
56. The Forever War, by Joe Haldeman
57. Small Gods, by Terry Pratchett
58. The Chronicles Of Thomas Covenant, The Unbeliever, by Stephen R. Donaldson
59. The Vorkosigan Saga, by Lois McMaster Bujold
60. Going Postal, by Terry Pratchett
61. The Mote In God's Eye, by Larry Niven & Jerry Pournelle
62. The Sword Of Truth, by Terry Goodkind
63. The Road, by Cormac McCarthy
64. Jonathan Strange, Mr Norrell, by Susanna Clarke
65. I Am Legend, by Richard Matheson
66. The Riftwar Saga, by Raymond E. Feist
67. The Shannara Trilogy, by Terry Brooks
68. The Conan The Barbarian Series, by R.E. Howard
69. The Farseer Trilogy, by Robin Hobb
70. The Time Traveler's Wife, by Audrey Niffenegger
71. The Way Of Kings, by Brandon Sanderson
72. A Journey To The Center Of The Earth, by Jules Verne
73. The Legend Of Drizzt Series, by R.A. Salvatore
74. Old Man's War, by John Scalzi
75. The Diamond Age, by Neil Stephenson
76. Rendezvous With Rama, by Arthur C. Clarke
77. The Kushiel's Legacy Series, by Jacqueline Carey
78. The Dispossessed, by Ursula K. LeGuin
79. Something Wicked This Way Comes, by Ray Bradbury
80. Wicked, by Gregory Maguire
81. The Malazan Book Of The Fallen Series, by Steven Erikson
82. The Eyre Affair, by Jasper Fforde
83. The Culture Series, by Iain M. Banks
84. The Crystal Cave, by Mary Stewart
85. Anathem, by Neal Stephenson
86. The Codex Alera Series, by Jim Butcher
87. The Book Of The New Sun, by Gene Wolfe
88. The Thrawn Trilogy, by Timothy Zahn
89. The Outlander Series, by Diana Gabaldan
90. The Elric Saga, by Michael Moorcock
91. The Illustrated Man, by Ray Bradbury
92. Sunshine, by Robin McKinley
93. A Fire Upon The Deep, by Vernor Vinge
94. The Caves Of Steel, by Isaac Asimov
95. The Mars Trilogy, by Kim Stanley Robinson
96. Lucifer's Hammer, by Larry Niven and Jerry Pournelle
97. Doomsday Book, by Connie Willis
98. Perdido Street Station, by China Mieville
99. The Xanth Series, by Piers Anthony
100. The Space Trilogy, by C.S. Lewis