The Supreme Court began its new term on Monday, setting the stage for potentially important decisions on everything from free speech to immigration. For the first time, the high court will have three women on the bench — justices Ruth Bader Ginsburg, Sonia Sotomayor, and the newly confirmed Elena Kagan, who replaces the retired leader of the court's liberal bloc, John Paul Stevens. Here are three big cases coming up and the legal issues at stake:

Gay-bashing at military funerals
The case: This term's marquee case may be a lawsuit by Albert Snyder, the father of a fallen marine, against the Westboro Baptist Church for protesting at his son's military funeral. Members of the Kansas church showed up at the ceremony with signs reading "God hates fags," because they believe war casualties are God's punishment for America's acceptance of homosexuality. Snyder won an $11 million jury verdict for emotional distress, but an appeals court threw out the award on First Amendment grounds. Now, Snyder is taking it to the Supreme Court.
The issues: Snyder has an uphill fight on his hands, say the editors of The Takeaway. "The Supreme Court has traditionally been very reluctant to impose limits on our freedom of speech, even offensive speech." But, like the debate over the mosque in downtown Manhattan, this case is special, says Furman University legal expert Rodney A. Smolla, as quoted by The New York Times. Free speech may be a fundamental right, but when it comes to Ground Zero and military funerals, "the cultural feeling is that each is close to a sacred space."

Keeping violent video games away from kids
The case: Video-game makers are fighting California's ban on selling violent games to minors. Lawyers for California Governor Arnold Schwarzenegger say these games can warp young minds. Lawyers for game makers say parents, not the state, should make that call. A lower court sided with the industry, so California is taking it to the Supreme Court.
The issues: The court should stand up for industry rights here, says Ilya Shapiro at Cato@Liberty. The "existing videogame ratings system" works better than a government ban. "Adding a level of governmental control, even if it were constitutional, would be counterproductive." But as a "videogame megafan and a noble anti-censorship crusader," says Darren Franich at Entertainment Weekly, even I can see the "positive side of the ban." Some kids are "stupid" enough to act out what they see on screen — at least this way, parents must buy their "gory" games for them.

Arizona's immigration law, part one
The case: The Supreme Court will make a decision not on the state's controversial SB1070 law cracking down on illegal immigrants, but on a 2007 measure imposing penalties on businesses that hire illegal immigrants. The issue is whether the law oversteps the state's authority and intrudes into an area — immigration — where the federal government has ultimate responsibility.
The issues: Whatever the court decides, says Kevin Johnson, Dean of the UC Davis Law School, quoted in the Christian Science Monitor, will signal how it might resolve the question of whether SB1070 tramples federal authority over policing U.S. borders. "This is potentially the biggest immigration ruling of the past 30 years." But this is just one of the 25 cases out of 51 from which Justice Kagan must disqualify herself, says Robert Barnes in The Washington Post, due to her tenure as solicitor general. If only eight justices hear the case, it could end up in a 4-4 lock — in which case the appeals court ruling in the government's favor will stand.