I've read (and loved) all of Laura Lippman's Tess Monaghan series, which features her greyhound Esskay. Does anyone know of any other books with greyhounds as regular characters?

Also looking for any novels featuring Cardigan Welsh Corgis - that might be little tougher!

The other dog mystery series I love is Susan Conant's Holly Winter malamute series....waiting for a new one to come out. Seems she's branched out into cat and chef mysteries - but I love the malamutes (and she mentions greyhounds sometimes, too!).

The series of books by Rita Mae Brown & Sneaky Pie Brown features a Corgi who, with his cat friends, helps to solve mysteries. The books are mostly  centered on horse and foxhunting activities but the cats and the Corgi are right in the action picking up clues that the humans don't even notice.  BTW, the dog and cats and various other animals can "talk" to each other. Sounds hokey but the books are pretty good mysteries.

the Rita Mae Brown books are what came to mind for me also for the corgis though I don't know what kind of corgi Tucker is. they're pretty good though; at least the first bunch are...I think I missed one later on and was kinda lost at some of the characters though the animals stay cute the whole time.and their talking we can read but to the people in the story it's animal noises like meowing /barking etc.

Emily Carmichael wrote a series with a Corgi. Actually she's an evil *itch that came back reincarnated as a Corgi to right the wrongs she did while she was a live. They are mostly romance/mystery. I can't remember the exact titles but one is called Diamond In the Ruff. I thought they were great!

There is also an inspirational book out called Conversations With My Dog which happens to be a Corgi. Sorry, I can't remembe the Author's name.

This probably isn't what you're looking for, but there is a graphic novel series called Korgi by Christian Slade.  

This is the phrase in the review that sold me on reading it : fire-breathing corgis.