I just received the latest Val McDermid mystery to check out, and I've had to put it away in the cabinet so I'm not tempted to start reading on duty. I enjoy all of her books, but the Dr. Tony Hill/Carol Jordan mysteries are the ones that I finish in one sitting. Tony Hill is a psychologist and criminal profiler who works with the British police - often DCI Carol Jordan. Tony is a character with many psychological problems of his own and the gruesome details are not for the faint of heart, but I find these books to be gripping mysteries. Many people also enjoy the TV series inspired by the books, Wire in the Blood. For reading purposes, start with the first book, The Mermaids Singing.
On this side of the pond (Boulder, Colorado), Stephen White's Alan Gregory series follows psychologist Gregory and his family and friends through sixteen books. They combine the fast-paced plot of a thriller with complex characterizations to form a series you'll want to follow from the beginning, with Privileged Information.
Finally, two of my favorite fictional characters to spend time with: Dr. Alex Delaware and his best friend, Detective Milo Sturgis, stars of Jonathan Kellerman's long-standing series. Alex is a consulting psychologist for Milo's cases with the LAPD and the city of Los Angeles becomes a vivid character to the reader. Alex is often reckless, but not tortured, an intelligent and compassionate person you enjoy having as a guide through these plot-driven investigations. I don't know that these have to be read in order, but if you share my affliction for having to start at the beginning, read When the Bough Breaks. I also highly recommend the audiobooks, read by John Rubenstein.