Institutional memory - there is great value in not reinventing the wheel every few years just because the ever-new crop of justices can't remember what a wheel is. I worked for a judge who could remember nearly every case for the preceding 20-ish years he had been on the court, and could find cases decided by other influential courts it would be unlikely anyone would have found using standard legal research. It wasn't that the cases always went his way, or that we relied on his memory to tell us what a case said - we always pulled the actual cases - but his grounding in the history of the court meant the decisions were relatively consistent over time. The law needs to be consistent so people who make decisions based on the law can rely on the rug not being pulled out from under them just because all of the institutional memory vanished.
Insulation from political influence. That may seem odd, but how a jurist performs on the bench often has little relationship to the party which appointed him. There are many factors which lead to this, but two of them are being completely disconnected from political influence (in the sense that once appointed you no longer rely on party affiliation as a job retention prerequisite), and working on the breadth of cases which come before the court over time with some of the best legal minds around (both your fellow justices, and the cream of every year's law school graduates as judicial attorneys). Justice O'Connor and Justice Kennedy were appointed by Reagan, and Justice Souter was appointed by Bush. Just to name a few recent examples, but it often takes time to mature into a view which is independent of the person/party who appointed you (and there are, of course, a few stinkers who never do).
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