My opinion of Rehnquist isn't all that important. Needless to say I was not a fan, and I will not venerate him in death. I don't believe that someone who believed in Plessy v. Ferguson and engaged in harassment of black voters (at least earlier in life) should ever have been on the supreme court.
But Rehnquist is dead and I take no joy in anyone's death. The question is what comes next. I think it's pretty clear that John Roberts will be confirmed as a supreme court justice. There's not enough solid facts about him for the Democrats to expend the necessary political capital to block him, and with two openings now available they need to save their strength in case someone truly heinous gets the new nomination. If Sandra Day O'Connor decides to stay on the court as a result of Rehnquist's death, a scenario that seems somewhat unlikely, this may shift, but for now his confirmation seems to be quite likely.
That being said it's interesting to me that Bush would nominate him as Chief Justice. I thought that that honor would go either to Scalia, for his rabidly conservative viewpoints, or to Clarence Thomas who would instantly become the nation's most prominent black conservative. I had expected Thomas, since he has obvious ties to Bush's father, he's younger than Scalia (Bush clearly wants to make his mark on the court, and he expects this chief justice to reign for quite some time) and the Republicans have made hay through use of prominent black conservatives to defray claims of racism and try to jar some of the African American vote from the hands of the Democrats. To choose Roberts brings up a bunch of issues. His youth is a definite positive, for the reasons above. It implies that Bush is more confident about Roberts' conservatism than many other Republican pundits, and it could potentially spark a power struggle within the court. Scalia and Thomas are both veterans of the Supreme Court while Judge Roberts has spent very little time on any bench, comparatively. His being vaulted ahead of them in line might rankle, especially since his youth makes it likely that neither Justice would ever get a shot at the Chief justice slot that at least Scalia seems to covet. With the opening of the papacy the Catholic church chose to go the opposite direction, putting an old man in charge in what is clearly going to be a transitional role, and I thought Bush would do the same.
It could also imply that Bush is aware of how low his political capital is and doesn't think he could push Scalia or Thomas through right now. That makes the potential nominee for the second slot intriguing as well. Many people think it will be Alberto Gonzalez, a good friend of the President's and an important conservative Hispanic. The problem is, of course, that Gonzalez is seen as Bush's lapdog, and wrote torture memos that bother those members of the Senate who still care about such minor inconveniences as the United States constitution and the Geneva Convention. He might be a tough sell, and it will be interesting to see whether Bush floats his name to see which way the wind blows, tries to ram him through, or goes for someone a little less controversial. Personally I'd guess the latter, but I wouldn't be shocked to see Gonzalez come up for nomination, especially now that the less troublesome Roberts will assuage liberals about the status of the chief justice slot.
As for what these changes will do to the actual court itself...well that's not clear. Certainly it will become more conservative and Roe Vs Wade will be placed in jeopardy, but the fact is that this was bound to happen after Bush was coronated for a second term. It was already a forgone conclusion.
Personally I think that this Supreme Court shift is the least of our worries as a nation. The court is made up of professional lawyers, and unless a complete crazy ideologue sneaks his way into the black robes it will run more or less the same on most of the cases that come before it. The ones that it rules the wrong way on can generally be countered with legislation. I am sorry that Chief Justice Rehnquist died, but I don't think his death will create a great crisis regarding the Supreme Court.