The story of a city and the stories in the city, with good action, good comedy, good music, and lots of pathos. 24 episodes, with a sort of bonus episode after 12 and 24. Aired in 2010. Available on Netflix and Crunchyroll.
It is hard not to compare Durarara to its spiritual predecessor, Baccano, and the overly forced cameos don't help much. But while Baccano is the intensive tale of a single train ride and the circumstances and passengers intersecting on the train, Durarara is the extensive tale of the town of Ikebukuro, which is a district of Tokyo in much the same way that Manhattan or Queens are districts of New York City. The genius of Durarara is the way in which it weaves, and often leaves unwoven, the disparate strands of its large cast. When following the main story in any given episode, we can often see the principle figure of the previous or next episodes running around, their chance encounters being explained by someone else's drama. Every character is unique and special and every character, even the most supernatural ones, feels more genuinely human than most real people I know. And when the show is over, you feel like you could call up Shizuo or Ryuugamine or Shinra and just hang with them like you have been for the last 26 episodes. The animation quality stands head and shoulders above most action shows, with even the supernatural violence being represented in a realistic way that respects real world physics. The music always fits, and is always of the highest quality. Speaking of which, the second intro song is actually a really bad cut of a really good song:
Both of these are "Complication" by Rookiez is Punk'd, a band with a general punk-metal sound, they have two albums on Amazon, and at least one of them is pretty good. The upper video has been chipmunked, but I can't find a better copy on Youtube. The lower video is a variation from their new album.
The second half of the show keeps this out of the top five, since it trades pretty heavily on surprises and twists that, after the first one or two, aren't actually that surprising. This worked out pretty well for me because on the re-watch I noticed that the show shines mostly in the characterization and in the interweaving of the threads of the city, things which can be enjoyed perhaps even more on a second run because you catch all the foreshadowing and you can see that the second act twists have all been laid out even as Mikado walks off the train in Episode 1. But if you are watching it for the surprises, the ending starts to drag because instead of spiraling into more twists as so many anime do it instead folds them all up, tidies everything, and actually resolves the conflict in an intelligent, emotional fashion that relies on neither deus-ex-machina nor improbably sudden realizations.
The greatest strength of Durarara is the depth and commitment to Magical Realism, the narrative notion that if the supernatural did exist, they wouldn't act like cartoons but like actual people. From the wholly supernatural headless rider to the fully normal Togusa there is no empty space on the continuum and yet none of the characters seem less real for being less realistic. It is hard to go into too much detail on this topic without spoiling the semi-remarkable characters, but overall it contributes to a very mature narrative that respects the viewer, respects the story, and respects the characters.
Obviously you should watch Baccano. And, just like the signs on the movie theater, you should try Darker than Black, a much more traditional narrative that has a similarly mature narrative. For a more upbeat and character driven experience, Stiens;Gate is peerless. Though really the problem is there aren't actually too many shows like this, both in scope and quality. You are probably better off going the complete opposite direction into something like Haibane Renmai before transitioning back into standard adventures.
Durarara stands head and shoulders above the crowd as a more intelligent and more profoundly characterized anime. This definitely belongs on anyone's must watch list. As a note, even though the show seems done in episode 24 (or 25, depending on how it is counting), go ahead an watch the final episode, because it makes the thematic connections much stronger. It does drag a bit before episode 20, but it really is worth getting through the slow patch for the finale.
Personally, based on how much I enjoyed it, I give Durarara a 9/10.