From the beginning of the show, there has always been controversy. Whether it was due to Bart's bad language or the T-Shirts bearing "Underachiever and Proud Of It", its been there and still doing it.
September 1990 - In an interview for People Magazine, United States Former First Lady, said about the Simpsons "the dumbest thing I've ever seen"
Early 1990 - A school principal from Ohio had banned the wearing of Simpsons T-Shirts with the phrase "Underachiever & Proud Of It" in his school entirely, leading to an entire story on national news
January 1992 - Former United States President said in a speech that "The nation needs to be closer to the Waltons than the Simpsons". Soon after, a commercial aired before the episode "Stark Raving Dad" with the Simpson family watching the speech and being shocked, and Bart replied "Hey, we're just like the Waltons. We're praying for an end to the depression too."
October 1992 - After "A Streetcar Named Marge" aired, residents of New Orleans complained of the defamatory lyrics in the episode labeling New Orleans as "home of pirates, drunks and whores". The chalkboard gag for the following episode was "I Will Not Defame New Orleans"
November 1992 - In "Marge Gets A Job", Bart uses Tourette's Syndrome as an excuse to get out of a test. Due to complaints, this is replaced with 'rabies' in syndication
January 1994 - After allowing students to name a new Elementry school in South Carolina to "Springfield Elementry" in a creative writing contest, the school board felt pressure from many parental groups that Bart was a bad role model. The school board was unaware of the namesake at the time of the decision and the name stayed.
Winter 2001 - After a brutaly violent Itchy & Scratchy Christmas comic (of course... it's Itchy & Scratchy) was printed in well over 50 newspapers, at least four of the newspapers dropped The Simpsons Weekly Comic entirely due to complaints.
March 2002 - The tourist board of Brazil threatened to sue The Simpsons and FOX for the depiction of Rio de Janeiro in the episode "Blame It On Lisa" which characterized it as a dirty, rat infested, crime-filled city. Soon after, Al Jean, the show's executive producer, formally apologized on behalf of the show and went without incident.
February 2003 - In a dream sequence two women representing sister colleges shared a sensual kiss that sent shock to viewers across the world.
'Till The End Of Time - Various religious groups have criticized The Simpsons for outlandish remarks and the treatment of Flanders