In no particular order:
1. Justice Scalia was not, in my judgment, the most "conservative" member of the current U.S. Supreme Court. He was out-flanked on the right by Justice Thomas and Justice Alito. (UPDATE: I'm amused to see that the NYT has published a chart based on an 'empirical' study that confirms what was admittedly my anecdotal impression based on reading cases.)
2. His most distinctive view--that the original public meaning (not intention of the framers) of the Constitution determines its application--has been adopted by almost no one in the judiciary, though he did succeed in making references to original meaning much more fashionable, even among liberals. (Citations to old dictionaries, as evidence of original public meaning, are now standard in court opinions, whereas they were infrequent at best thirty years ago.) He was more consistently committed to this view than most proponents of a "theory of interpretation," though he made exceptions when it suited his moral and political commitments. But his general commitment to the approach often belied his "conservative" reputation. So, for example, Justice Scalia's majority opinion in Crawford v. Washington (2004) (which I happened to teach just last week) was the single biggest windfall for criminal defendants since the 1960s. Justice Scalia held that the constitutional right of a criminal defendant to "confront" the witnesses against him demands the exclusion of many kinds of out-of-court statements that, in the past, easily came into evidence under various exceptions to the rule prohibiting hearsay. An extension of this ruling also now requires prosecutors to produce in court for cross-examination the forensic experts and lab technicians who conduct lab testing of all kinds related to a criminal case. Attempts to limit the impact of Crawford on the prosecution of criminal defendants have been led by the "liberal" Justice Sotomayor, herself a former prosecutor. (ADDENDUM: Another notable opinion, perhaps not what one would have expected, was his dissent in Hamdi.)
3. The U.S. Supreme Court, as all "insiders" know, is not a regular court, but more akin to a super-legislature, though one of limited jurisdiction. There are two limits on that jurisdiction: first, it can only make law on issues that are brought to the court; and second, existing law often restricts the range of possible new laws the Court can make. But because issues that come to the Court are usually ones where the law is quite indeterminate, and where moral and political judgment is required to resolve the case, the moral and political predilections of the super-legislators are of crucial importance in their selection. This, of course, is why the Republicans are already threatening not to approve a nominee (in the unrealistic hope that they will win back the Presidency), and the Democrats are keen to push forward: opportunities to add a super-legislator don't come up that often, after all, and their terms can extend for decades. On almost every major and controversial decision in recent years--on gay marriage, on campaign finance, on affirmative action, on the right to bear arms--the actual decisions were all legally optional, and a different mix of political and moral views on the Court would have changed the outcome.
4. Without Scalia, there are four usually "liberal" votes in the super-legislature (Breyer, Ginsburg, Kagan, Sotomayor), three usually "conservative" votes (Alito, Roberts, Thomas), and one sometimes "conservative," sometimes "liberal" vote (Kennedy). Scalia was, of course, a usually reliable "conservative" vote, and when they could get Kennedy's vote, the conservatives ruled. This, of course, is why Scalia's replacement is of crucial political significance: if a "liberal" super-legislator is appointed, then the Court becomes majority "liberal" for the first time in many decades. Justice Kennedy's influence also fades dramatically.
5. Until Scalia's seat is filled, there is a risk of tied decisions, which will leave the status quo intact wherever they occur.
Thoughts/comments from readers?