This is a legendary anime series about some instant classic characters, the Lupin gang. This is amazingly ahead of it's time, being the first anime starring criminals, the first gritty comparatively more realistic anime with guns and such. Not just for anime, it's ahead of it's time in general.
Most importantly, it's still a joy to watch nearly 40 years later. Lupin is the cool, laid back antihero. This laid back style, helped by the very cool soundtrack, is still influential today in titles like Cowboy Bebop. Lupin has other sides to him too of course, he has an ego, and he'll laugh like a maniac and take on any challenge. And of course, he gets pretty excited when there are ladies around, especially Fujiko.
The supporting characters are great here. You have Jigen, Lupin's partner and best friend. He's very cool himself, a smooth criminal, but he's also the voice of reason, a more mature criminal. Then you have Fujiko, the classic femme fatale cat burglar, she is Lupin's love interest, and often his rival. Then there's Goemon, the renegade samurai with a strong moral code, who can cut anything. And of course, Inspector Zenigata, who tirelessly dedicates his life to capturing Lupin.
Lupin is episodic, featuring 23 self contained stories. Although there is one plot that takes two episodes early on, with Goemon out to defeat Lupin. One episode Lupin is in prison, another time him and the gang have explosive watches put on that they can't take off. These are all great stories.
An interesting thing about this series is that it has two different feels to it, depending on who is directing. Masaaki Osumi directs episodes 1-7, 9, and 12. These are the more dark and gritty episodes, and sometimes have a melancholy feel. These episodes are amazing, giving us the depth that the Lupin characters are built on.
The founders of Studio Ghibli, Hayao Miyazaki and Isao Takahata, direct episodes 8, 10-11, and 13-23. These episodes are also superb, with a more fun and upbeat feel, closer to what Lupin is known for today. You can tell Miyazaki is involved when Lupin starts saving cute damsels in a gentlemanly heroic way.
All in all, Lupin III is a classic series, which is still going strong today with movie specials. I recommend checking this out, it's must see anime.