There are many good recommendations already. Two American writers not mentioned are John Katzenbach and John Sandford.
Katzenbach doesn't have a recurring character and each of his novels is different in style and tone from the others. But, all his novels are very well written and the plots are uncommon. Some may find Katzenbach a touch dark. Four novels by Katzenbach that should satisfy the mystery/crime fiction fan: State of Mind, the Analyst, Madman's Tale, and the Wrong Man. Someone is neglecting his website as it doesn't seem to mention the most recent of his novels.
John Sandford (real name: John Camp), like Katzenbach and Michael Connelly (of the Harry Bosch novels) is a former journalist. He's most known for a series of about 20 novels with the recurring character Lucas Davenport, a character that should please any Rebus fan. His writing is very good, very wry.
I don't think anyone mentioned Minette Walters. I'm not sure I'm a fan, but her books deserve consideration.
Another American of note is Dennis Lehane. Particularly good are Mystic River and Shutter Island. Lehane also has a series of novels featuring a couple Boston detectives, but they are mostly too cute for my taste.