For series, there's the world-building; falling completely in love with a world and getting to stay for more than a single book.
The characters have a lot of time to develop; with forming relationships and they have more time for personal growth which is always a big win for me.
Standalones have the benefit of being shorter (i.e., less of a time commitment).
There's no waiting; no screaming at the last page of the book wondering WTF and having to wait an undetermined amount of time.
You also don't have to worry about being disappointed by books to come which is always a plus.
That being said I am 100% a huge follower of series. I own a substantial amount of series and I started off pretty much reading series. From my mom reading me, Harry Potter by J.K. Rowling:
To me reading A Series of Unfortunate Events by Lemony Snicket, The Boxcar Children by Gertrude Warner,
To in middle and high school discovering my deep love of all things Teen Paranormal Romance with the Mortal Instruments series by Cassandra Clare, Vampire Academy by Richelle Mead, Wonderous Strange by Lesley Livingston and Hush, Hush by Becca Fitzpatrick.
Even now with all my unfinished series: see the full link to unfinished series here, I love reading series. I love being in a world for over 300+ pages. For watching the characters struggle, grow, and kick butt for 10,000,000+ pages.
Now that's not to say I don't enjoy the occasional standalone novel. I love those too: Some Boys by Patty Blount, The Host by Stephanie Meyer (since I doubt Stephanie will ever release any more even though she said she would), Ache by S.M. Soto, or Only a Breath Apart by Katie McGarry.
I think part of being a reader is just finding what you love and not worrying so much about the label of being a series or standalone fan.
What about you? Are you a hard and fast standalone only type of person?
Do you fall madly in love when you find out the book you picked up has eight more books tied to it?