So... is Sakamichi no Apollon finished or not?
NO, it is not finished.
Why?
The anime finished after the manga:
Anime finished: June 29, 2012
Manga finished: January 28, 2012
... But MangaUpdates contains information about the anime adaptation and indicates that it is incomplete.
Watching Order (by release date)
Here you have all the anime relations we detected ordered by release date, so you can see the reason for this status in context and also use it as watching order.
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Synopsis
Sakamichi no Apollon follows Kaoru, a classically trained pianist who constantly moves and struggles to fit in. When he arrives in a new town for high school, he meets Sentarou, a charismatic delinquent with a passion for jazz.
Sentarou's love for jazz inspires Kaoru to explore this new genre, leading him to befriend Ritsuko, whose family owns a record shop with a basement jazz club.
As Kaoru begins playing jazz piano, he discovers the joy of connecting with others through music and starts to come out of his shell. The anime explores themes of friendship, music, and personal growth as these three students navigate their high school lives and form lasting bonds.
The story centers on their summer together, suggesting it will be a formative and memorable experience for Kaoru and his newfound friends.