The term also inevitably will bring a return to a topic the justices themselves find uncomfortable - the possibility one or more will pick this year to quit. The court has maintained the same cast for a remarkable nine years and counting - the longest streak in modern history - and retirement speculation builds each year.
The justices shrug off or refuse to answer questions about their plans, and some have complained privately that there is an almost ghoulish preoccupation with their ages and health.
There are emotional topics aplenty in the term that opens Monday. During the next several months, the justices will hear a case that echoes a bitter fight two years ago over the constitutionality of school voucher plans. This case asks whether states can withhold scholarships from students pursuing religious training.
The court is expected to rule soon in an enormously complicated case that asks whether new regulations for campaign donations and political advertising violate the Constitution's guarantee of free speech. The ruling will affect how candidates raise and spend money in next year's federal elections.
The justices also will hear a case about brass-knuckle politics as practiced by legislators who draw the boundaries for congressional districts. The case looks at the effects of gerrymandering.
"The court is always on dangerous ground when it ventures into politics," said Walter Dellinger, a Washington lawyer and former acting solicitor general in the Clinton administration. "The court never knows where it makes things better or worse."
The campaign finance case probably is giving the justices fits. They held an unusual, one-day session last month to get a head start on it. Many lawyers predict that as hard as they try, the justices will produce a hash of overlapping opinions that redirect the way money flows in campaigns without reducing it.
"I think the court will not give us a clear and neat answer," said Erik S. Jaffe, a First Amendment lawyer and former law clerk to Justice Clarence Thomas.
Overshadowing those cases, and probably any other the court may hear this term, is a church-state fight involving the Pledge of Allegiance and whether it should be recited in public schools.
The Bush administration, a California school district and an atheist with a school-age daughter have asked the court to rule whether the phrase "one nation, under God" unconstitutionally entangles God and government.
The justices could say as soon as Monday whether they will hear the case, which has caused a national uproar since a California appeals court ruling last year siding with the father.
Many lawyers and law professors who follow the court predict the justices will try to resolve the pledge issue as quietly as possible, without hearing the merits of the case. For example, the justices could reverse the decision on procedural grounds, or send it back to a lower court.
Taking on the case as a full-blown constitutional test could open a can of worms the court probably prefers to keep capped for now, said Steven Shapiro, legal director of the American Civil Liberties Union.
"It will put the court right back in the middle of the culture wars, which I suspect is where they do not want to be," he said.
In its most recent term, which ended in June, the court struggled with culturally divisive questions of race and homosexuality. The ordinarily conservative court ended up preserving affirmative action in college admissions and striking down laws criminalizing gay sex.
There is nothing as socially contentious among the cases the court has already accepted for review in the new term, although forthcoming rulings are expected to have long-lasting effects in such areas as the rights of the disabled and consumer protection.
The court continues its examination of states' rights and the balance of power with the federal government, and has a heavy docket of cases about crime and punishment.
Several cases involve allegedly heavy-handed police tactics. In one case police arrested everyone in a car where drugs were found, even though the officer had no reason to suspect all occupants were involved in anything illegal. In another, police set up a roadblock to try to find witnesses to a hit and run accident, but instead nabbed an allegedly drunk driver.
The court still has room for about 25 to 30 more cases that it can hear and decide before next summer. In addition to the pledge question, the court could add a Bush administration appeal in a California medical marijuana case, a free speech case about children and online smut, and challenges to government policies after the Sept. 11 terror attacks.
The court will observe its tradition of convening the new term on the first Monday in October, but with a twist. For the first time, the court announced it will not hold oral arguments on opening day because the Jewish holiday of Yom Kippur falls on that day.
Two of the nine justices are Jewish: Ruth Bader Ginsburg and Stephen Breyer.
By Anne Gearan