Should a school be able to curb a student's speech online because the content is available on campus? A case in the 3rd U.S Circuit Court of Appeals sets a precedent in protecting off-campus online speech of a student.
According to ThinkFree 
“In 2005, while a high school senior in the Hermitage School District in western Pennsylvania, 17-year-old Justin Layshock created a fake Facebook profile parodying the high school principal. He was suspended for 10 days and, with help from the American Civil Liberties Union, sued the school district.
In 2007, a federal judge sided with Layshock and ruled that school districts cannot discipline students for off-campus speech.”
But the decision of 3rd Circuit Court of Appeals does not signal a trend. President Obama's Supreme Court nominee Judge Sonia Sotomayor (2nd Circuit Court of Appeals) sided with the majority in the decision that says
“schools had the authority to regulate off-campus online speech because that speech can disrupt the functioning of the school”
University of Nevada, Las Vegas student paper The Rebel Yell  discusses the issue of student's online free speech in length, citing instances where students in various American universities have been targeted for disciplinary action for what they said online.
“In 2007, T. Hayden Barnes, a former student at Valdosta State University in Georgia, campaigned against the planned construction of two parking garages on the university’s campus.
Part of his opposition was a collage he posted on his Facebook page called the “Zaccari Memorial Parking Garage” — named after and featuring the university’s then-President Ronald Zaccari.
The school viewed it as a threat, and the student was expelled.”
After a lawsuit the university reversed its decision.
As the world of communications evolves,the debate over what is covered by First Amendment is also changing to include social networking and sites like Twitter.Speaking about twitter and online free speech, recently a Chicago woman was sued for a “tweet” she sent out which her landlords claim were defamatory.
“Horizon Group Management sued Amanda Bonnen Monday for publishing a false and defamatory tweet on Twitter May 12.
According to the suit filed Monday in Cook County Circuit Court Bonnen wrote an update that said “Who said sleeping in a moldy apartment was bad for you? Horizon realty thinks it's okay.”
PBS discusses online free speech in this video ,with regards to social networking site like Facebook and micro blogging platforms like Twitter.