I've been reading detective fiction since I was 10. It's my comfort blanket and I return to my favourite authors again and again.
I don't like it too gory and find some of the American authors and Val McDermid a bit too much graphic for me but VMcD does write well so worth a try if you're not as squeamish as me.
My favourite authors are Ian Rankin (Rebus as others have mentioned but also his latest character Malcolm Fox - not quite as good as Rebus yet but may get there) and P.D.James.
A recent discovery which is very witty and well written is the Montalbano series by Antonio Camilleri. Based in Sicily and about 15 available in translation at the moment. Particularly good if you also love food as he spends a lot of time describing his delicious meals :) really evocative of Sicily, and I'm so glad I discovered this series.
Michael Dibdin's Zen novels are also set in Italy and well worth a read, especially as you can spend the whole of your reading time dreaming of the ravishing Rufus Sewell who played him on tv :)
I love Agatha Christie - a bit dated but utterly classic. I have been working my way through the female Golden Age writers recently - Ngaio Marsh, Margery Allingham and Dorothy L Sayers - and Christie is undoubtedly the best, much less dated than any of them. My favourites are The Body in the Library and Murder on The Orient Express. Her Tommy & Tuppence novels are less well known but equally worth a read.
Another series worth digging out is Amanda Cross's Kate Fansler. I love the lead character - a New York professor and rather feminist.
I agree on Peter James by the way - was recommended to me as I live near Brighton but he is so mysoginistic that I can't bear to give him my money.
If I think of more, I'll let you know 