Yes, but so far not successfully.
In March 2007, comedian Carol Burnett filed a lawsuit against 20th Century Fox, claiming that it was a trademark infringement for her Charwoman cleaning character to be portrayed on the show without her permission. Besides that, Burnett stated that Fox violated her publicity rights. She asked for $6 million in damages. On June 4, 2007, United States District Judge Dean Pregerson rejected the lawsuit, stating that the parody was protected under the First Amendment, citing Hustler Magazine v. Falwell as a precedent.
On October 3, 2007, Bourne Co. Music Publishers filed a lawsuit accusing the show of infringing its copyright on the song "When You Wish Upon a Star", through a parody song entitled "I Need a Jew" appearing in the episode "When You Wish Upon a Weinstein". Bourne Co., the sole United States copyright owner of the song, alleged the parody pairs a "thinly veiled" copy of their music with antisemitic lyrics. Named in the suit were Twentieth Century Fox Film Corp., Fox Broadcasting Co., Cartoon Network, MacFarlane, and Murphy; the suit sought to stop the program's distribution and unspecified damages. Because "I Need a Jew" uses the copyrighted melody of "When You Wish Upon a Star", without commenting on that song, Bourne argued that it was not a First Amendment–protected parody per the ruling in Campbell v. Acuff-Rose Music, Inc. On March 16, 2009, United States District Judge Deborah Batts held that Family Guy did not infringe on Bourne's copyright when it transformed the song for comical use in an episode.
In December 2007, Family Guy was again accused of copyright infringement when actor Art Metrano filing a lawsuit regarding a scene in Stewie Griffin: The Untold Story, in which Jesus performs Metrano's signature "magic" act involving absurd, faux magical hand gestures while humming the distinctive tune "Fine and Dandy". Metrano's suit claims this performance is protected under terms of the United States' Copyright Act of 1976. 20th Century Fox, MacFarlane, Callaghan and Borstein were all named in the suit, which is still ongoing.