(that is, under the age of thirty when the award was announced or retrospectively might have been announced)

Hugo winners under 30:

Hal Clement (1922-2003) 1946 retro-Hugo, Best Short Story, Uncommon Sense
Isaac Asimov (1920-1992) 1946 retro-Hugo, Best Novel, The Mule
George R.R. Martin (1948-) 1975, Best Novella, A Song for Lya 
C.M. Kornbluth (1923-1958) 1950 retro-Hugo, Best Novelette, The Little Black Bag
Samuel R Delany (1942-) 1970, Best Short Story, Time Considered as a Helix of Semi-Precious Stones
Damon Knight (1922-2002) 1950 retro-Hugo, Best Short Story, To Serve Man
Roger Zelazny (1937-1995) 1966, Best Novel, ... And Call Me Conrad 
Larry Niven (1938-) 1967, Best Short Story, Neutron Star 
Spider Robinson (1948-) 1977, Best Novella, By Any Other Name
Spider Robinson (1948-) 1978, Best Novella, Stardance (with Jeanne Robinson, who was already 30 by the time award was announced) 
Joan D. Vinge (1948-) 1978, Best Novelette, Eyes of Amber

Nebula winners under 30:

Ted Chiang (1967-) 1990, Best Novelette, Tower of Babylon 
Samuel R Delany (1942-) 1966, Best Novel, Babel-17
Samuel R Delany (1942-) 1967, Best Novel, The Einstein Intersection 
Samuel R Delany (1942-) 1967, Best Short Story, Aye, and Gomorrah 
Vonda N. McIntyre (1948-) 1973, Best Novelette, Of Mist, and Grass, and Sand 
Samuel R Delany (1942-) 1969, Best Novelette, Time Considered as a Helix of Semi-Precious Stones
Roger Zelazny (1937-1995) 1965, Best Novelette, The Doors of His Face, the Lamps of His Mouth 
Roger Zelazny (1937-1995) 1965, Best Novella, He Who Shapes
Rachel Swirsky (1982-) 2010, Best Novella, The Lady Who Plucked Red Flowers Beneath the Queen’s Window
Alexei Panshin (1940-) 1968, Best Novel, Rite of Passage
Michael Moorcock (1939-) 1967, Best Novella, Behold the Man
Spider Robinson (1948-) 1977, Best Novella, Stardance (with Jeanne Robinson, who was already 30 by the time award was announced)
Lisa Tuttle (1952-) 1981, Best Short Story (declined), The Bone Flute
Gordon Eklund (1945-) 1974, Best Novelette, If the Stars Are Gods (with Gregory Benford who was 34 when award was announced)