Amicus Briefs at the Cert Stage:
Over at Slate, Adam Chandler has an interesting essay on the use of Supreme Court amicus briefs at the cert stage. (In English, those are written legal arguments filed by "friends of the court" — that is, folks other than the litigants themselves — on whether the Supreme Court should take a case.)

  By way of background, such briefs are almost always in support of the petition. They are designed to get a law clerk's attention and make the dispute appear more nationally important, and therefore increase the chances the Court will grant cert. In particular, amicus briefs make the stack of briefs that the clerk receives more formidable: They send a message to the clerk writing the pool memo that says "this one is important and probably has a chance, so set aside some time for it." Plus, amicus briefs are identified in pool memos: Their arguments are usually summarized in in a short paragraph after the arguments of the parties. For these reasons, cert-stage amcius briefs can increase the chances that the Court will "flag" the petition as something unusually important. Almost no one files amicus briefs against certiorari, as it would very likely backfire: Such a brief would tell the Court that you think the case is so important that you've written in to keep the Justices out, which only makes them more interested.

  Some stats from the essay:
  Between May 2004 and August 2007, nearly 1,000 private organizations filed cert-stage briefs. Only a few make it a habit—just 16 groups filed eight or more early-bird briefs a piece. Ten of those top amici serve business interests and conservative causes. They include the Products Liability Advisory Council, the Pacific Legal Foundation, and the National Association of Manufacturers. And the king of the amici, the U.S. Chamber of Commerce, filed 55 briefs over the period studied, or about 17 each year.
  Among the top 16 cert-stage amicus filers, the National Association of Criminal Defense Lawyers is the only one that might be considered a liberal interest group. It ranked second to the Chamber of Commerce with 33 briefs. The American Civil Liberties Union tallied just two cert-stage amicus briefs during the three years under review.
  I wonder if cert-stage amicus briefs might be a good project for some of the law school clinics that are cropping up and are looking for cases. It's less sexy to write a cert-stage amicus brief than a merits brief, of course. But such briefs can have a recognizable impact by explaining the stakes of a case in a way that petitioners themselves often can't.