I prefer reading stand-alone as compared to the series.
However, the question is regarding the favorite series. I was deeply engrossed in Greek Mythology after reading Percy Jackson and the Olympians series by Rick Riordan; so I guess that would be my favorite book series so far. It is only that the sequel to this series, The Heroes of Olympus, has not been able to bring about the same reading experience for me.
Things I liked about Percy Jackson series:-
1. Percy Jackson as the narrator was very tactful but still it was clear that he was a young person who was dealing with situations he had never imagined to be true. It had provided a depth to the plot line and a surprise element as well.
2. There were limited characters and it was fun to read about them. The camp life and the quests were wonderful with inclusions of the popular figures of Greek mythology like Medusa, hydra, furies, the gods of Olympus as well as the minor gods and the demigod heroes.
3. There was a feeling of adventure; it was as if the readers were also fighting against the Titans along with the characters. The geography covered was diverse as well.
I have also enjoyed reading The Hunger Games Series by Suzanne Collins and Harry Potter series by J.K. Rowling.