By Matthew Davis
BBC News, Washington
All the attention is currently on the make-up of the US Supreme Court, but the new judges will not be long into their term before they have to tackle a range of important social issues.
The BBC News website looks at some of the most controversial cases in a calendar packed with contentious issues such as abortion, assisted suicide and capital punishment.
On 5 October the court will hear a challenge to Oregon's one-of-a-kind law that allows doctors to help terminally ill patients die more quickly, in the case of Gonzales v Oregon.
Assisted suicide is an important issue to conservative Christians, core supporters of the president.
The Bush administration wants to overturn rulings by two courts that protect Oregon doctors from federal punishment for aiding suicide.
Oregon's voters approved assisted suicide in a referendum on the Death with Dignity Act - used by 170 people since 1998 - and the case will be a test of the power of states to make their own laws within America's federal system.
There are five death penalty cases scheduled, or waiting to be scheduled, the most contentious of which concerns a Tennessee case (House v Bell) in which a death row inmate claims new DNA evidence exonerates him.
Judges will have to decide how strong newly discovered evidence of innocence must be before it warrants a new hearing in a federal court.
In the case of Kansas v Marsh, scheduled for 7 December, the court will consider the constitutionality of Kansas' death penalty law, which requires that a death sentence be imposed when a jury finds that aggravating circumstances and mitigating circumstances have equal weight.
Recent years have seen a steady decline in the numbers of death sentences handed down in the US, and a series of legal steps limiting the use of the ultimate sanction.
The assumption is that a more conservative Supreme Court would be less inclined to whittle away at use of the death penalty.
The main abortion case before the court this term involves New Hampshire's parental notification law - which provides for parents to be told when minors have abortions.
The law has an exceptions for situations in which the life of the mother is threatened, but not merely her health. It also enables judges to override the notification process in the minor's best interests.
A ruling on Ayotte v Planned Parenthood of New England does not pose a threat to the landmark case that enshrined abortion rights - Roe v Wade - but it gives the court a chance to make it harder to contest restrictions on the procedure.
It will be heard on 30 November.
Supreme Court justices may also decide to hear a case that involves the Bush administration's attempt to reinstate a law that bans a type of late-term abortion.
Pro-choice groups say abortion rights are being eroded in the US and the fact that Mr Bush has had the chance to nominate two new justices to the Supreme Court has electrified the debate on this controversial subject.
On 6 December there is an appeal that involves gay rights, as part of a protest against the Pentagon's "don't ask, don't tell" policy on gays and lesbians in the military.
In hearing the case Rumsfeld v Forum for Academic and Institutional Rights, the court will review an appeals court ruling that strikes down a federal law which cuts off funding to universities that don't treat military recruiters as favourably as other employers.
Some law schools have refused assistance to military recruiters because they say the "don't ask, don't tell" policy contravenes their anti-discrimination rules.