Jojo's Bizarre Adventure started as a manga by Hirohiko Araki and has been running since 1986. The series is called that because of how every protagonist (tentatively) shares the nickname of Jojo. There are multiple story arcs, with each of them starring a different generation of the Joestar bloodline. Parts 1, 2, and 3 are all (very well) adapted fully into anime by David Production. Currently, the manga is up to Part 8, and Part 4 is being released as an anime adaptation with a new episode every Friday.
The first story arc. Stars Jonathan Joestar, gentleman and powerful Ripple user, as he fights against Dio Brando, his stepbrother turned vampire, and his minions.
Joeseph Joestar, grandson of Jonathan, is a natural born stand user and a polar opposite of his grandfather when it comes to his personality. Alongside Caeser Zeppeli, he defends the world against a powerful race of ancient superhumans.
Arguably the most popular part; it is adapted into both an OVA and into 2 seasons on TV. The fighting style of the Ripple is replaced with the new concept of Stands, a manifestation of one's own fighting spirit. Part 3's main protagonist is Jotaro Kujo, grandson of Joseph Joestar, as he and his allies journey to Egypt to challenge Dio (same antagonist as Part 1) and save Jotaro's mother.
The Bow and Arrow is introduced in this part; it is an artifact that grants Stand abilities to those who are struck with it and survive. Certain villains in the town of Morioh are vying for control over the arrow so that they can create Stand users at will. To stop them and protect the town is Josuke Higashikata, the illegitimate son of Joseph Joestar.
Giorno Giovanna's dream is to become an influential gangster (he calls it being a gang-star.) So, he joins Pasionne, an italian mafia that is comprised of Stand users with the primary motive of making the streets a better place. This part is probably the most controversial part among fans, as many people believe that Part 5 isn't good at all.
Jolyne Kujo, daughter of Jotaro Kujo, is framed for murder and gets thrown in prison. She is antagonized by Enrico Pucci, a priest who was influenced by Dio.
Johnny Joestar is a paraplegic who is a contestant in the Steel Ball Run race, a transcontinental horse race for a ton of money and fame. He follows Gyro Zeppeli with the goal of learning the secret to his steel balls (he uses spinning steel balls as a weapon) because he believes that learning about Gyro's secret will enable him to walk again.
A mysterious amnesiac sailor with four testacles is discovered by Yasuho Hirose to be buried beneath the dirt in Morioh. They search throughout the town for clues to his identity. Part 8 is still ongoing and is probably around halfway done.
The anime can be watched pretty much anywhere; kissanime is a good place to watch it if you don't mind disabling adblock. Parts 1 & 2 are both featured in Jojo's Bizarre Adventure (2012), Part 3 is separated into 2 seasons (both called Stardust Crusaders) and Part 4 is currently airing.
My favorite part is part 7. I think it has the best protagonist (I named one of my birds after him) and antagonist but unfortunately it has a bit of a rocky start. I also really like where part 8 is heading. Some people think that it's on its way to surpassing part 7 but I disagree.