Of course, it is term-paper season, but it seems as though the biggest reason people look at the LII's Supreme Court collection is an interest in the Justices themselves. Those coming to the site by way of a search on "supreme court justices" or something similar accounted for around 15,000 of the 367,540 visits to the collection last month. They spend roughly twice the average amount of time on the site, too. Unsurprisingly, the next-largest cluster of searches we can identify involves Roe v. Wade.
As far as individual Justices go, Sandra Day O'Connor is the most-searched-for, with Clarence Thomas a distant second. Ruth Bader Ginsburg is in third place. Interestingly, searchers typically type out Justice O'Connor's name in full ("Sandra Day O'Connor"), but favor a terse, lower-case approach to Scalia ("scalia"). Only one of the 367,540 searched for "nino".