If Steven Spielberg is the Jewish icon of the movies and Philip Roth the Jewish icon of the novel, then Neil Simon is certainly the Jewish icon of the play: if, in final Jeopardy! Alex asks (or is it answers? we always get this confused) something along the lines of Jewish... playwright... yadda yadda yadda you can confidently scribble Simon's name and hope for the best.
Two of the best known Simon plays, because they have been turned into movies, would be Brighton Beach Memoirs and Biloxi Blues. Both actually feature the same character — one Eugene Jerome — and are part of the Eugene trilogy (Broadway Bound only got a TV movie and so may as well have not existed). And both introduced us to a young actor.
Biloxi Blues gave us Matthew Broderick (actually Broderick starred in both on Broadway, but again, no one gives a crap about a play) who went on to star in such popular and well received gems as Project X, The Cable Guy, and Inspector Gadget. Also some films that are actually watchable. Seriously.
The other, Brighton Beach Memoirs gave us Jonathan Silverman (see!! we were getting there!) who went on to do... Ummmm... Well there's... OK, well, Weekend at Bernie's is a movie some people seem to have...
Oh whatever they can't all be winners. At least Silverman is better than the kid they got to play Eugene in the TV movie of Broadway Bound: his best known acting credit is for an ABC After School Special called "Don't Touch."