First: my book group chose A FAR CRY FROM KENSINGTON and I am pleased because that is the one I really wanted and I am looking forward to rereading it.
So, series characters, or should I say detectives, as I'm thinking mostly of crime fiction here. On the whole I like them. If you are reading for pure pleasure and relaxation it can be nice to know what you are getting into. It's like meeting up with old friends: Morse, Travis McGee, Kinsey Milhone, we know some of their history, we're look forward to seeing them again and finding out what they'll get up to next. There are advantages for the writer too. You have done the spade work and have brought your fictional terrain and its characters into being, you're at home there, and you too want to know what these people will do next. Now that I've nearly finished a stand-alone, I can't wait to get back to my Cassandra series.
But there are disadvantages too. Sometimes the readers go on loving Hercule Poirot or Sherlock Holmes when the writer is heartily sick of them and could happily murder them and of course that's just what Conan Doyle did. It is hard to maintain the same high standard in novel after novel and perhaps it's more obvious in a series novel when you don't. I read a couple lately that were a little disappointing, though I am a fan of both writers. In Donna Leon's THE GIRL OF HIS DREAMS and Qui Xiaolong's THE MAO CASE, Commissario Brunetti and Inspector Chen retain their old charm, but in the first the plot was a bit thin and the second was paced too slowly.
To end on a positive note one series that is going from strength to strength is Stieg Larsson's Millenium series. THE GIRL WHO PLAYED WITH FIRE is terrific and shows that he was just getting into his stride with THE GIRL WITH THE DRAGON TATTOO.