This is one of my personal favorites. It doesn't necessarily have the best animation or the best story, the music I find hardly memorable, but I adore it "just because". There are quite a few things that aren't made totally clear in the anime, which I'd like to help you out with. First, however, let me say that the opening with its ritual sacrifice isn't my favorite part, but it does actually have meaning. I usually try to ignore it after the first episode, and I hope it doesn't turn you off to the rest of the show.
So in the beginning, you'll see a bunch of guys hanging out in the desert, and although they talk about it, the first time I saw it, I wasn't exactly clear on what the heck was going on. The oldest guy's (the grizzled-looking blonde one) daughter is in the hospital because of some severe illness. This was caused by the evil vampire-like guy named Dio. This daughter has a son named Jotaro (JoJo), and he's the guy in blue with the hat and funky chain on his collar. The others are basically their buddies who they interact with from time to time in the manga.
What kind of anime would this be, if the guys hanging out in the desert looking for a vampire didn't have super-powers? So, they have a certain kind of power called a "stand". Ever get X-men hologram cards out of cereal boxes? Well, stands are sort of like that -- without the card. Each of these guys calls up his stand, which sort of projects out of their bodies or around their bodies like a hologram. These stands are each related to a tarot card and usually have a color in their name. JoJo's is Star Platinum, his grandfather's is Hermit Purple. You'll get to see them all eventually, but here's a rundown of what they can do:
Star Platinum: It is very fast with heightened senses; JoJo can use SP to give him better vision or hearing or to move very quickly. JoJo is good at getting just what he needs from his stand, and he has superb control over it and himself.
Hermit Purple: Basically, it's thorny vines, which are somewhat useful. Additionally, and not seen in the anime, really, the hermit can create a protective shield around the user.
Magician's Red: This looks like a red-feathered eagleman and has fire powers as well as the usual super strength.
Silver Chariot: Pontaleff's stand is a wrinkly guy in a suit of armor with a fencing foil. It has a very rapid attack, which is basically all you see it do in the anime. (Pontaleff isn't exactly the brains of the outfit.)
Heirophant Green: You won't really get to see this until later episodes. It can fly away from Kakkyoin, but it is connected to him by tubes seemingly filled with green fluid. If you look closely, the stand is actually a suit filled with green fluid. Its attack is a cool machine-gun like barrage of emerald-like stones. Kakkyoin can do some other things with it too, which you'll see.
The Fool: The "new guy" has this fearsome power. It's sand-related, and the user is obnoxious to say the least.
The third episode is my favorite because JoJo uses cunning and mind games to defeat an opponent on whom brute force won't really work. Episode 4 or 5 (I forget) has the bad guy "Vanilla Ice" (check out the heart-shaped kneepad he's got). While he's got a wanky name and dresses like a dork, he's very powerful. The only thing I don't really like about the show is in the end. Just when you think they've beaten Dio with their smarts, he comes back for another round and they have to resort to a brute-force power battle. Still, it's pretty cool. Overall, they use their brains much more than force to beat the other stand-users they face, who are sometimes almost as clever as JoJo's little band.
Interestingly, in the early manga, they don't have stands at all. They're just tough guys. (The grandfather is the main character in the second part, which I believe is where stands first appear. The OAVs cover the third arc.)
Oh, I almost forgot to explain the title: the grandfather is Jonathan Joestar, and the grandson is Kujo Jotaro, and it's certainly bizarre.