JOANNE AKALAITIS, an important and controversial figure in American theater for nearly two decades, has succeeded Joseph Papp as artistic director of the New York Shakespeare Festival, a position Mr. Papp has held since he founded the organization 37 years ago.Ms. Akalaitis will preside over the downtown Public Theater and Central Park's outdoor Delacorte Theater, where free performances are presented every summer. After a year as Papp's artistic associate, she takes on her new responsibilities at a time when the institution faces severe financial pressures, stemming partly from Papp's refusal to accept funding from the National Endowment for the Arts in the wake of censorship disputes not directly involving the festival. The future of some ambitious projects initiated by Papp, such as an all-inclusive Shakespeare Marathon, is likely to remain in doubt until Akalaitis has time to reassess them. Before her association with the Shakespeare festival, Akalaitis was a founding member of Mabou Mines, a group of theater artists with experimental leanings. Akalaitis created what still may be her most celebrated production with this organization: "Dead End Kids: A History of Nuclear Power," a multimedia work (that was later made into a movie) that expressed an antinuclear message through visual spectacle and stylized performances. She has also done extensive work outside the Mabou Mines framework - earning particular attention for her productions of socially critical dramas by German playwright Franz Xaver Kroetz, including "Through the Leaves" and "Request Concert," and works by Samuel Beckett, who publicly renounced her approach to his "Endgame" six years ago at the American Repertory Theater in Cambridge, Mass. Although she is well-known for a lack of interest in Broadway-type commercialism, Akalaitis has been unwavering in her commitment to theater as an art form - insisting that her avant-garde image does not preclude a love of Shakespeare, of mainstream American playwriting, and even of TV soap opera. In a casual conversation last year, I deplored the state of the Broadway scene, and she was quick to respond that "we have to stay loyal to theater," despite the shortcomings that burden it and the temptations posed by more currently fashionable media. Her new position promises to begin an exciting period for theater-lovers of all inclinations.