The classical music establishment has always been divided about Gershwin. In his own time it was quite radical for a composer to have his music played in Broadway theaters, symphony halls, jazz nightclubs and Hollywood sound studios, especially one who had no formal musical training, and not everyone was quick to accept that he had a legitimate place in all those venues. Igor Stravinsky greatly admired the Concerto in F, Dmitri Shostakovich compared Porgy and Bess favorably to the operas of Mussorgsky, and he also received encouragement (tinged with professional jealousy) from Ravel and Schoenberg. But Prokofiev hated the concerto, Virgil Thomson declared that Gershwin "has not and never did have the power of sustained development" (though he later waxed rhapsodic about Porgy and Bess) and even Leonard Bernstein, while saying of Gershwin that "I don't think there has been such an inspired melodist on this earth since Tchaikovsky," and calls the concerto "the work of a young genius who is learning fast," dismissed Rhapsody in Blue as "a string of separate paragraphs stuck together - with a thin paste of flour and water."
What's interesting about this is that in some ways Gershwin was ahead of his time. Today's composers have largely discarded traditional notions of development in their compositions and have no compunction about crossing the line between "classical" and "popular" music - that debate is ancient history to composers like Nico Muhly, who at the age of 29 is two years older than Gershwin was when he wrote Concerto in F, and who, with the formal musical education Gershwin lacked (including a Master's from Juilliard) has written music for the New York Philharmonic and the Boston Pops, written music for films (including Best Picture nominee The Reader), and served as an arranger for several rock bands. Gershwin helped paved the way for today's music scene, in which music of different degrees of formality can peacefully coexist, whether in the concert hall, the Broadway theater, or the nightclub.
Here's a rare newsreel clip of Gershwin himself playing I Got Rhythm at the opening of the Manhattan (now Ed Sullivan) Theater, August 1931:
And here's a short animated film, directed by Una Lorenzen, set to Nico Muhly's composition "It Goes Without Saying":