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 .