These are mystery series written in the 1950s and earlier. Some of these series continued for many decades. Some of them are old enough to be considered public domain now.
When authors began writing mystery stories specifically for children, they discovered that kids were drawn to book that showed other children and young people as the heroes of the stories with little help from adults. Some adults were critical of books where young people got into trouble or had adventures with no adult supervision, but children liked the thrill of the stories and the sense of independence. Many of the early series were specifically “boy detective” or “girl detective” series, depending on who the main detectives in the stories were. Some of the series listed here are creations of the Stratemeyer Syndicate.
“Boy Detective” Series
Brains Benton is a young genius who investigates crimes along with his friend, Jimmy Carson. By George Wyatt. 1959-1961.
Hardy Boys Mysteries
Two brothers, Frank and Joe Hardy, solve mysteries in their East Coast town of Bayport and around the world. By Franklin W. Dixon, A Stratemeyer Syndicate series. 1927-Present.
“Girl Detective” Series

A young nurse solves mysteries as she completes her training, serves during World War II, and moves to different jobs. “Cherry” is a nickname for Charity. 1943-1968.
Felicia attends boarding school and solves mysteries with her friend and room-mate, Joan. By Bernard Palmer. 1958-1971.

Kay Tracey is a teenage detective who solves mysteries with her friends. A Stratemeyer Syndicate series. 1934-1942, Reissued 1951-1984.
Nancy Drew Mysteries
Nancy Drew encounters and solves mysteries with her friends in her hometown of River Heights and around the world. By Carolyn Keene, A Stratemeyer Syndicate series. 1930-Present.

An orphan girl in the early 20th century grows up to become the owner of her own film company in Hollywood. Along the way, she solves mysteries with her friends at school, on vacation, and later, on filming locations, and helps the war effort during World War I. A Stratemeyer Syndicate series. 1913-1934.
A classic mystery series featuring a girl and her group of friends who solve mysteries and support good causes. Created by Julie Campbell and continued by other authors. 1948-1986.
Detective Family Series

Two pairs of fraternal twins have adventures and solve mysteries. Early books were more adventure/general fiction than mystery, but the series evolved over time. Early books in this series are public domain and are available on Project Gutenberg. A Stratemeyer Syndicate series. 1904-1992.
Four children who lived alone in a boxcar after the death of their parents are taken in by their grandfather and solve mysteries everywhere they go. 1924, 1942-Present.
The Happy Hollisters
A family with five children solves mysteries. By Jerry West, A Stratemeyer Syndicate series. 1953-1969.
Detective Clubs and Friends
A group of friends solve mysteries with their pet Scottie dog. Also called the Five Find-Outers and Dog By Enid Blyton. 1943-1961.
The Lone Pine Club is a group of friends who love nature and investigate mysteries. By Malcolm Saville. 1943-1978.