Durarara!! is one of those tricky series—I first saw it as an anime and it’s based on a light novel series. The anime also has a manga adaptation, which is a little backwards. I quite enjoyed the anime, I haven’t encountered a translation of the light novels yet, and I recently discovered and read what exists of the manga.
Durarara!!‘s anime is a complete, plot-threads-wrapped-up twenty-five episode series which I at first thought was an original series with no manga/light novel source material. I was surprised to discover that the light novel series is in fact still ongoing, including several plot arcs and characters that just aren’t in the anime. The manga adaptation is also still ongoing, although it’s much farther behind—the chapters that have been released so far (about fifteen or two bound tankobons’ worth) don’t cover even half of the relatively short anime. The art is cute and very like the animation, though, and I’m enjoying reading it so far, even if the release schedule is awfully slow.
No matter what, I definitely recommend you check out Durarara!!—it’s a smart, action-y, mystery series with friendship, the supernatural, horror, high school romance, grown-up romance, and lots of interesting characters so there’s someone everyone will love. If I had to compare it to a movie, I’d say it was similar to The Princess Bride in that it has something for anyone and everyone and it’s very tightly written. There are epic plot twists, tons of Crouching Moron Hidden Badass folks (one of my absolute favorite tropes), and, unlike a lot of anime, you don’t have to be a dude to be awesome—in fact, the arguably most powerful character in the series is female. This anime is the first one I recommend to anyone, anime fan or not, when they ask me for series recommendations.
That said, I don’t think it’s worth it to read the manga if you haven’t seen the anime first. The manga is so slow-going that you could watch the whole series several times over before the manga gets to the real meat of the plot. I usually never recommend this, because most series that end before their manga does (for example, FMA, DNAngel, the first Hellsing series) end a little wonkily since they just have to run with what they have instead of following the mangaka’s original story to its proper conclusion. But, since the manga is less the source material and more the novelization of the anime, there’s no reason not to check out the anime first.