The Frabjous wonder of a good series - of reading a book, knowing that more will follow with the same characters and fantastic writing.
Of course Harry Potter comes to mind instantly, as well as Moomins, Tolkien - starting with The Hobbit of course - and the Dido Twite books. In each series, an adventure happens and ends rather satisfactorily at the end. JK Rowling and Tolkien went one step further and introduced a common thread, a continuing siege or adventure that kept readers returning for more.
Destroy the Ring!
Still, each volume of the series is, of itself, a good read with a beginning, middle, and an end.
Trust me, as an author of a series, this is a very hard thing to accomplish. You want the readers to be able to pick up any book and begin to read, but usually you really have to start at the beginning.
Of the above, for sheer genius in creating compelling story arcs and likable, living characters, I must go with JK. When I started The Deathly Hallows, I thought there was no WAY she could resolve every issue, especially with all those Horcruxes to be destroyed. Yet, resolve them she did. The woman is a goddess.
On the Indie front, my favorite series is Darkness Rising by Ross Kitson. Emelia is the main character, and she begins as a lowly servant in a castle. Soon she is propelled into a series of adventures, and she discovers hidden resources of strength and bravery.
It's all very epic and fantastic. Kitson makes Emelia spring to life right from the start. He has done a lot of world building; like JK Rowling, his universe (Nurolia) has been imagined with maps, languages, and characters. Kitson, a doctor in the UK, painstakingly illustrates them all, so the book is a journey through an imaginary country.
And - joy! Kitson has just started another series, called Infinity Bridge. This one is a steampunk read, with loads of urban fantasy. I devoured the first book and can't wait for the next.
And then there are those books that SHOULD be a series but are not .... cough ... Jonathan Strange and Mr. Norrell ... we are still waiting...