Just adding that while I do think they tend to appear in connection to the police, they aren't always. I can think of many examples that fit the trope, but aren't owned or operated by police:
Batman has a ton of databases on everything with ludicrous amounts of detail and information. It's often pointed out that these are not just police-related. Several are just his own work (somehow) (Hence him solving crimes the cops can't). Batman's not a cop, but he's still an example.
A magical example: The Dresden Files
, Harry has a Spirit called Bob The Skull, in Harry's own words, Bob is a magical sentient computer. Bob's used the same way a magical database, but regarding the supernatural. Also used to solve crimes. Overlaps with Great Big Book of Everything
Perhaps some sort of split/Super Trope
One supertrope "X is used to identify stuff. Sometimes to fight crime. Or to ID and defeat the Monster of the Week
." and another for "Police Procedural having Databases on stuff no sane man would make a database of" (ie: "I've put the half eaten hot dog on the national registry of hot dog saussages to find what hot dog stand the murderer worked at!")
edited 14th Jan '12 1:57:19 PM by Ghilz