The current U.S. Supreme Court, while by tradition called the "Rehnquist Court" after its ailing chief justice, is really the "O'Connor Court", because Justice Sandra Day O'Connor, who announced her resignation Friday, effective upon the appointment of a successor, is the pivotal vote on the nine member body. For more than a decade, the constitutional law of the United States has been dictated, overwhelmingly by Justice O'Connor's views.
More often than not, she is the deciding vote in a split between the court's four "liberals", Stevens, Souter, Ginsberg and Breyer, and the court's four "conservatives", Rehnquist, Scalia, Thomas and Kennedy. A more nuanced analysis can be found at SCOTUS Blog.
There is plenty of debate raging right now over who will be nominated to replace Justice O'Connor. Whoever it is, however, will be appointed by George W. Bush, and it is almost a certainty that whoever is nominated will be to the political right of not just Justice O'Connor, but also Justice Kennedy, who is the second most common swing vote. Likewise, when conservative Chief Justice Rehnquist retires or dies, and it is almost certain that this will happen before the end of George W. Bush's term, given Rehnquist's thyroid cancer, he will also, almost certainly, be replaced by a Justice to the right to Justices O'Connor and Kennedy.
The mixed performance of Democrats in fighting nominees to the U.S. Court of Appeals, resulting in the confirmation of hard core conservatives to these important posts, says to me that while there may be some limits on Bush's ability to get any nominee of his choice through the Senate, that there are certainly plenty of judges to the right of both Kennedy and O'Connor who can and will be confirmed.
In a nine member body that make decisions by majority vote, the only vote that really matters is the median vote. O'Connor's resignation makes it almost a certainty that this vote will be Justice Kennedy's vote. So, until Justice Stevens retires, you can count on the nation's jurisprudence looking a whole lot like that of Justice Kennedy. This will be a more conservative stance on a great many issues, although key decisions like Miranda and Roe will likely remain in tact during his watch.