I'm always looking for new writers and nothing beats a personal recommendation. There have been a lot of writers mentioned here that I've not heard of, so I have lots to try tracking down through the local library to try for myself. In Canada I think it is easier to get American books than UK books, so I may not be able to find some of those mentioned. One of the nice things about the internet is the international borders coming down.
Books that give me a sense of place (one of the reasons I like the Rebus books) are very appealing to me. Since I've never been rich enough or unencumbered enough to travel as much as I'd like, I like seeing the world through books.
Michael Connelly's Harry Bosch series essentially cast Los Angeles as a character similar to the way Edinburgh is a virtual character in the Rebus books. Like Rebus, Bosch is in the loner hero tradition, particularly in not quite fitting in with police regimentation, but he's a bit more "out there" than Rebus. I am afraid Mr. Connelly might not be quite sure to do with Harry at this point though, as the last few books haven't been nearly as strong as the earlier ones. I haven't read his new book yet though.
Another writer who makes me feel as though I am "there" (although I have never been) is Tony Hillerman in his Joe Leaphorn & Jim Chee mysteries. Like Rebus, Joe Leaphorn is an older hero, in this case a Navajo Tribal policeman, with little manpower to cover vast and scarcely populated areas. Unlike Rebus's creator, I believe that Mr. Hillerman was of an age with his hero when he created him, but as the books grew into a series, he introduced the young maverick Policemen Jim Chee. Although Leaphorn eventually retires, the "legendary lieutenant" recurs enough to keep Chee's life interesting.
The other recommendation made by a few people here that I must heartily concur are the Robert Crais books. I admit to initially feeling a character named "Elvis" was a bit much, but Elvis Cole is such a good character he quickly knocked down my reservations and wormed his way into my heart (mostly with his humor). More compelling is his taciturn partner/friend Joe Pike. Very good characters, and although the plots are lighter than Rankin's, they are page turners.
If you're into the macabre there is Michael Gruber. Even though I'm not as a rule, his characters and storytelling are so compelling I can't resist.
I've only discovered Frances Fyfield in the last few years, and what I have been most impressed with is the way she can force me to look at things differently. Although I tend to read books more than once (and as I get older, the time between when it has fallen out of my mind enough to re-read it has shortened) I had to re-read her novel "The Nature of the Beast" immediately upon finishing it. Never done that before or since.
The last author I'll plug (for now
) is one that you will either love or hate. Carl Hiassen has written some of the best black comedy mystery books ever. They tend towards... uh, seriously twisted... which if you can take it with a smile you'll love. For many years he was a journalist covering Florida politics and corruption, and I think he had a lot of fun meeting out judgments to callous thoughtless greedy creeps in his books. Unfortunately he's taken a break from the really twisted (but screamingly funny books like "Lucky You" and "Stormy Weather") to write a couple of children's books and a golf book.