The Nobel Prize was a Human award given to people who performed breakthrough research in physics, chemistry, and other fields.
One of Jean-Luc Picard's ancestors was awarded the Nobel Prize in Chemistry. (Star Trek Generations)
Jonathan Archer reminded T'Pol not to be primarily concerned with getting a Nobel Prize and the scientific exploration of microsingularities encountered by the Enterprise in 2151, but more with the well-being of Trip Tucker and Malcolm Reed. (ENT: "Shuttlepod One")
Tucker sarcastically replied he wouldn't take a Nobel Prize home soon, when asked if he had finished rewriting the physics books after encountering different laws of nature in the Delphic Expanse in 2153. (ENT: "Anomaly")
Doctor Richard Daystrom was awarded the Nobel Prize (as well as the Zee-Magnees Prize) in 2243 for his invention of duotronic computers. (TOS: "The Ultimate Computer")
When the USS Voyager was transported from 2373 to 1996, Chakotay speculated that if he had to stay in this time, he'd make archaeological discoveries in Central America earning him a Nobel Prize. (VOY: "Future's End, Part II")
According to the Star Trek Encyclopedia (4th ed., vol. 2, p. 85), the Nobel Prize were "
... annual awards established by Earth chemist Alfred Nobel
), recognizing outstanding achievemens in science, literature, medicine, and peace."
As of 2016, there is no Nobel Prize for Archaeology.