Also, you don't have to have poor little rich girls or private school drama to have a good series, although a couple of the series listed here have some of those elements as well. I have included a few books with sequels that might eventually become series. These books are all for older teen readers.
Sisterhood of the Traveling Pants by Ann BrasharesI loved this series the first time I read it, and I continue to love it seven years later.
Peaches by Jodi Lynn AndersonThese girls are the Sisterhood of the South.
Jessica Darling by Megan McCaffertyI can't think of a girl more different than me, but somehow Jessica Darling managed to make me understand her.
Gingerbread by Rachel CohnThis is my poor little rich girl series, but the main character doesn't stay downtrodden (or filthy rich) for long.
Gallagher Girls by Ally CarterThis is my boarding school drama series, only there girls know how to kick some butt.
Scarlett Martin by Maureen JohnsonTwo books thus far, but I believe at least one more is on its way.
Lulu Dark by Bennett MadisonI sure hope this Prada-wearing Nancy Drew has a couple more books in her future.
I'm also giving the Confessions of Georgia Nicolson books by Louise Rennison an honorary mention.