Susan Cooper: The Dark Is Rising Series

This is not a typical "series." It's a five-book sequence of fantasy novels written for young people.
Main Characters: Merriman Lyon, Will Stanton
Setting: England
Bold type indicates a book I've read.

Over Sea, Under Stone (1965) [See Review]
The Dark Is Rising (1973) [See Review]
Greenwitch (1974) [See Review]
The Grey King (1975) [See Review]
Silver on the Tree (1977)

Maud Hart Lovelace: The Betsy-Tacy Books

Main Characters: Betsy Ray and her best friends for life, Tacy and Tib
Setting: Mainly Hill Street, although the later books branch out a bit
Bold type indicates a book I've read.

Betsy-Tacy (1940) [See Review]
Betsy-Tacy and Tib (1941)
Betsy and Tacy Go Over the Big Hill (1942)
Betsy and Tacy Go Downtown (1943)
Heaven to Betsy (1945)
Betsy in Spite of Herself (1946)
Betsy Was a Junior (1947)
Betsy and Joe (1948)
Betsy and the Great World (1952)
Betsy's Wedding (1955)

Arthur C. Clarke: The Space Odyssey Series

This is a series of science fiction stories and novels that take place over a fairly long period of time and in different parts of the universe. In general, the main characters and settings differ in each of the works.
Bold type indicates a book I've read.

"The Sentinel" (written in 1948, first published in 1951 as "Sentinel of Eternity")
"Encounter at Dawn" (first published in 1953)
2001: A Space Odyssey (1968)
2010: Odyssey Two (1982)
2061: Odyssey Three (1987)
3001: The Final Odyssey (1997)

Frank Herbert: The Dune Saga

Main Characters: Duke Leto Atreides, head of House Atreides; Lady Jessica, concubine of the Duke, mother of Paul and Alia; Paul Atreides, the Duke's only surviving son; Alia Atreides, Paul's younger sister; many, many others
Setting: Mainly the planet Arrakis
Bold type indicates a book I've read.

Dune (1965)
Dune Messiah (1970)
Children of Dune (1976)
God Emperor of Dune (1981)
Heretics of Dune (1984)
Chapterhouse: Dune (1985)