Just another GR refugee. Other than that, I had a stroke in 2004, and read almost anything I can get my hands on, though I have a particular weakness for history, mystery, and historical fiction.
If we're talking a literal "literary detective," it must be Thursday Next!
If we're talking favorite detective in literature, I find it hard to pick just one. I love Matthew Shardlake (a Tudor lawyer, working first for Cromwell, and then for Cranmer and Queen Catherine Parr - his cases sometimes involve murder investigations), Barbara Havers (I don't love Lyndley as much as Elizabeth George does; but no book of hers can have too much Havers), Mary Russell Holmes, Nero Wolfe and Archie Goodwin (confound it!), Nicomides and Diotima (who work for Pericles), Sherlock Holmes, and, of course, the magnificent Lord Peter Wimsey.