The earliest book I could find in the series was Blood Rites, by Jim Butcher, which is the sixth book. Quick synopsis: Harry Dresden is a wizard PI who can’t speak Latin, and has lots of magic. His friend Thomas, a vampire (but not the blood-sucking kind), asks him for a very small favor, which turns out to involve the porn industry and curses (and maybe more vampires) and gets very complicated very fast. Mentors and assassins turn out to not be who they seemed to be, and Harry’s family is a bit more complicated than he thought. He accidentally adopts a magic puppy. And somewhere there’s a mystery to be solved.
Or so I assume. After about fifty pages, I gave up and skipped to the end. The characters were two-dimensional and boring, there was no clear plot (or rather there were too many plots), and the writing was pedantic. Perhaps the earlier books in the series are better. In any case, as I was reading it, there were several places where I thought "this would probably work better on screen".
Turns out I was right. My friend with cable was very nice and taped four shows for me, which I sat down and watched one after the other. And the most obvious difference that makes the shows work where the book didn't is the exclusion of the vampires - and most of Harry's past. Oh, it's there, and one of the shows has a couple flashbacks to when Harry was a kid, but it's very minor and doesn't interfere with the flow of the story. Thomas' role of friend is filled by Bob, the sort-of-ghost who is little more than reference book and spy in Blood Rites. The rapport between Bob and Harry was my favorite thing about the TV show.
Leaving aside the changes in characters and plot lines, the fundamental difference between the show and the book is quite simple. Where the book doesn't seem to know whether it's mystery, horror, or soap opera, the core of each episode of the show is clearly a mystery, and that's all. A little less grand in scope, perhaps, but a lot easier to follow.
Bottom line? If you're interested in mysteries and magic, watch The Dresden Files - it's great fun. But don't bother with the books. (And that's something I didn't think I'd ever find myself saying.)