Don't know why this anime was split into parts 1 and 2. I just watched episodes 1-26, so I'm going to review it as one show.
It starts with a rich family (the Joestars) adopting a poor boy named Dio. Dio is the same age as the Joestar's son, Jonathan, and they become fierce rivals at everything trying to get the attention of Jonathan's father. Initially, Dio is better at everything, but as they grow up, Jonathan catches up to Dio, making him bitter and twisted. One day, he finds a stone mask, that when attached to his face, transforms him into an evil vampire...
The shows stretches over 3 generations of Joestars and each son is nicknamed Jojo. They spend their lives fighting vampires and other, stronger immortals.
What I really liked about this show was the humour. The characters were all great and the animation and action scenes were awesome, but the humour turned what could have been a dark, horror type story into something really fun. Normally, I'd prefer them to have left out the humour and gone down the dark path, but in this case, it really works well. Definitely worth a watch!