But what happens when the issue is less clear and a judge has the appearance of a conflict, but no personal stake in the outcome of a dispute? The court is considering a case that asks whether the Constitution requires judges to step aside in that instance.

The justices met in private Friday to discuss a lawsuit over a coal contract in West Virginia in which a state Supreme Court justice rejected calls to step aside because the leader of one company in the case spent more than $3 million to help him get elected.

Justice Brent Benjamin twice was in the majority in 3-2 decisions overturning a $50 million jury verdict against Massey Energy Co. Don Blankenship, Massey's president, chairman and chief executive officer, was a key Benjamin backer. Two other state court justices recused themselves from the case the second time it was under consideration.

The losing party, Harman Mining Corp., says the appearance of bias by Benjamin is so strong that Harman's constitutional rights were violated. Former Solicitor General Theodore Olson is representing Harman.

The court agreed with the plaintiffs, who said the state's marriage law discriminates against them because it applies only to heterosexual couples, therefore denying gay couples the financial, social and emotional benefits of marriage.

Eight same-sex couples sued in 2004, saying their constitutional rights to equal protection and due process were violated when they were denied marriage licenses.

The court ruled unanimously on Wednesday that an agreement leaving the final decision up to the ex-wife must be followed.

Dr. Laura Dahl, a pediatrician, and her former husband, Dr. Darrell Angle, an orthodontist, had attempted to conceive through in vitro fertilization.

After several failed attempts, the couple gave up and left the embryos with Oregon Health & Science University under an agreement that spelled out how they would be stored.

Dahl decided to have the embryos destroyed, but Angle had argued they should be donated to other couples trying to conceive.

In an opinion by Presiding Judge Rex Armstrong, the court ruled there is a contractual right to determine the fate of the embryos as personal property.

But Armstrong noted there is little guidance on who gets to make that decision in a divorce, so the court relied on a 1998 New York state case that held agreements on what to do with embryos after in vitro fertilization are binding.

Armstrong — noting the ruling in New York — said that it should be the parents, "not the state and not the courts, who by their prior directive make this deeply personal life choice."

Dahl said she opposed her ex-husband's recommendation that the embryos be donated to another woman for implantation because she did not want anybody else to raise her child.

Dahl also was concerned that any child born as a result of implantation might later wish to contact the son who she and Angle had previously conceived naturally.

The court noted that Angle "does not argue that the agreement itself is ambiguous or invalid for public policy reasons" and affirmed a Clackamas County Circuit Court ruling that he agreed his ex-wife would make the final decision.

The first day of the court's new term, which is set in law as the first Monday in October, included denials of hundreds of appeals. Chief Justice John Roberts opened the new session in a crowded courtroom that included retired Justice Sandra Day O'Connor.

Last term, the justices handed down several opinions that limited state regulation of business in favor of federal power. Several justices posed skeptical questions in this term's first case, whether federal law prevents smokers from using consumer protection laws to go after tobacco companies for their marketing of "light" and "low tar" cigarettes.

The companies are facing dozens of such lawsuits across the country.

The federal cigarette labeling law bars states from regulating any aspect of cigarette advertising that involves smoking and health.

"How do you tell it's deceptive or not if you don't look at what the relationship is between smoking and health?," Chief Justice John Roberts said during oral arguments on the case.

Three Maine residents sued Altria Group Inc. and its Philip Morris USA Inc. subsidiary under the state's law against unfair marketing practices. The class-action claim represents all smokers of Marlboro Lights or Cambridge Lights cigarettes, both made by Philip Morris.

The lawsuit argues that the company knew for decades that smokers of light cigarettes compensate for the lower levels of tar and nicotine by taking longer puffs and compensating in other ways.

A federal district court threw out the lawsuit, but the 1st U.S. Circuit Court of Appeals said it could go forward.

The role of the Federal Trade Commission could be important in the outcome. The FTC is only now proposing to change rules that for years condoned the use of "light" and "low tar" in advertising the cigarettes, despite evidence that smokers were getting a product as dangerous as regular cigarettes.

Without comment, the justices declined to consider Englewood, Colo.-based Dish's appeal.

In January, the U.S. Court of Appeals for the Federal Circuit agreed with a lower court that digital video recorders distributed by Dish, formerly known as EchoStar Communications Corp., violated the software elements of Alviso,Calif.-based TiVo's patent. The ruling overturned the lower court's finding that Dish also infringed on the patent's hardware elements.

TiVo issued a statement saying it was "extremely pleased" with the Supreme Court's decision and said company lawyers would press for Dish to pay financial damages.

TiVo sued in 2004, alleging that EchoStar, a satellite broadcaster, infringed on TiVo's patented technology that allows viewers to record one program while watching another. EchoStar Communications changed its name to Dish in late 2007.

TiVo pioneered digital video recorders that allow viewers to pause, rewind and fast forward live television shows.

The lower court had ordered Dish to shut down the 3 million digital video recorders used by its customers because they use TiVo's technology, but that order was put on hold pending appeal.

Dish Network has said that the ruling would not affect its customers because the company had developed and distributed new DVR software that "does not infringe the Tivo patent at issue in the Federal Circuit's ruling."

Without comment, the justices declined to consider whether the jury foreman's conduct violated the rights of Jimmie Lucero, an Amarillo, Texas, man sentenced to death after being convicted in the shotgun slayings of three neighbors at their home in 2003.

The state of Texas argued that the Bible passage merely duplicated instructions of the trial court. The Texas Court of Criminal Appeals found the introduction of the Bible into the jury room to be "harmless error."

A Texas jury took about five hours to decide on the death penalty for Lucero.

The two jurors who switched their votes said the reading of the scripture and its content had no impact on their votes.

During deliberations, the foreman read aloud from Romans 13:1-6, which states that everyone must submit to authority and that those who do wrong should be afraid, for a ruler is "God's servant, an agent of wrath to bring punishment to the wrongdoer."

Lucero was convicted in the killings of 71-year-old Pedro Robledo, his 72-year-old wife, Maria, and their daughter, Fabiana, 31.

The 2nd U.S. Circuit Court of Appeals said Thursday that Sheik Mohammed Ali Al-Moayad and Mohammed Mohsen Zayed, convicted of supporting terrorists, can have new trials. The three-judge panel took the unusual step of ordering the transfer of the case to a new judge.

The men were convicted in federal court in Brooklyn after a six-week trial in early 2005 on charges of conspiring to support al-Qaida and Hamas, supporting the Palestinian group and attempting to support al-Qaida. Their trial featured testimony by an FBI informant who set himself on fire outside the White House, saying he wanted more money from the FBI.

Al-Moayad, 60, was sentenced to 75 years in prison. Zayed, 34, was sentenced to 45 years.

The appeals court said the defendants were prejudiced by testimony from a Scottish law student who told of a deadly suicide bombing on a bus in Tel Aviv and by an American citizen of Yemeni heritage who attended an al-Qaida training camp in Afghanistan in 2001.