The following is a list of the novels that have won both the Hugo and the Nebula. There are countless (that means I didn't bother to count) others that have been nominated for both awards, but only these have taken home both trophies. The dates are the copyright years for each, and do not necessarily reflect the actual year the awards were won. Please note that there are four different authors who have accomplished this feat twice each - Ursula K. Le Guin, Arthur C. Clarke, Joe Haldeman, and Orson Scott Card - with Card the only one to do it in consecutive years. EDIT: And now Connie Willis joins that list.
Dune ¹ (1965) - Frank Herbert
The Left Hand of Darkness (1969) - Ursula K. Le Guin
Ringworld (1970) - Larry Niven
The Gods Themselves (1972) - Isaac Asimov
Rendezvous with Rama (1973) - Arthur C. Clarke
The Dispossessed (1974) - Ursula K. Le Guin
The Forever War (1975) - Joe Haldeman
Gateway (1977) - Frederik Pohl
Dreamsnake (1978) - Vonda N. McIntyre
The Fountains of Paradise (1979) - Arthur C. Clarke
Startide Rising (1983) - David Brin
Neuromancer (1984) - William Gibson
Ender's Game (1985) - Orson Scott Card
Speaker for the Dead (1986) - Orson Scott Card
Forever Peace (1997) - Joe Haldeman
Doomsday Book ² (1998) - Connie Willis (reviewed by ekt)
American Gods (2001) - Neil Gaiman (reviewed by Galen)
Paladin of Souls - (2004) Lois McMaster Bujold
The Yiddish Policeman's Union (2008) - Michael Chabon
The Windup Girl ³ (2009) - Paolo Bacigalupi (reviewed by Galen)
Blackout / All Clear (2010) - Connie Willis (reviewed by Galen)
¹ Dune tied for the Hugo with This Immortal (Roger Zelazny).
² Doomsday Book tied for the Hugo with A Fire Upon the Deep (Vernor Vinge).
³ The Windup Girl tied for the Hugo with The City and the City (China Miéville) (reviewed by Galen)
