The Nobel Prize was a prestigious award given on Earth in the 20th and 21st centuries. Its recipients included scientists such as Clifford Jones and Alistair Gryffen, as well as John Brent. (TV: The Green Death, TV: The Custodians, PROSE: Time and Relative)
Dr Fendelman once suggested that Adam Colby would win a Nobel Prize for his work in palaeontology. (TV: Image of the Fendahl)
Sarah Jane Smith hoped that her journalistic work exposing the international arms trade might earn her a Nobel Prize. (PROSE: Interference - Book Two) According to one account she did address the Nobel Academy in 1998, at that time using the name Sarah Jane Morley. (PROSE: Christmas on a Rational Planet)
In 2008, The Pharm hoped to win the Nobel Prize once they'd developed Reset for human use. (TV: Reset)
Prior to 2009, Professor Sir Rupert Silverman was nominated for the Nobel Prize for Physics. (TV: The Eternity Trap)
Behind the scenes
All Nobel Prize winners explicitly named as such in Doctor Who or related fiction have been scientists. (John Brent's status as a scientist is implied, rather than explicit.) Other Nobel laureates, such as Barack Obama, have appeared, but their status as Nobel Prize winners has not been mentioned.