Elfen Lied is just bad. That's pretty much common knowledge in every anime community. The story is weak, the characters had no depth, the humor was forced, the character design was terrible, and the voice acting was bad enough to kill the entire show on its own.
So why is this show still enjoyable? It has been argued that Elfen Lied is supported entirely by gore and nudity, and yes, these aspects certainly do appeal to a wide range of male viewers; but it's nothing short of ludicrous to suggest that gore and nudity alone can support a show. If that were the case, people would browse deviantart or other similar sites instead of watching Elfen Lied.
So what makes this show so special? Well, here's one take on the reason behind Elfen Lied's popularity.
First of all, the plot. Elfen Lied is driven entirely by emotion and not logic. If you sit back and think about everything that happened from a logical perspective, the entire story will fall apart. Elfen Lied is one of those shows that you switch off your brain to enjoy. By maintaining a high degree of suspension of disbelief, this show becomes an emotional rollercoaster with huge ups and downs.
Secondly, the characters. Elfen Lied is a bit of a character driven show, but the characters aren't anything special. The characters are basically two dimensional cardboard cutouts who aren't really trying to interest the viewer, and the voice acting does not make them any better. So why is it still a character-driven show? Well, it's a character-driven show in the sense that the show is driven by sympathy for the characters. Every single character in this show is in an endless cycle of despair - and it's heartwarming as well as heartbreaking to watch their struggles in a living hell.
Thirdly, the sound. This show has absolutely terrible voice acting, whether you watch the English or Japanese dub. Roughly 70% of the time, even the voice actors themselves sounded bored. However, during the "tearjerker" moments, the voice acting does get a lot better. Nothing outstanding, but at least good enough for the viewer to overlook any faults. In addition, the show has an absolutely amazing OP and soundtrack that more than compensates for the usually poor voice acting.
Finally, the fanservice and gore: It's true that fanservice and gore are a two of the most important ingredients for the making of Elfen Lied. Still, a lot of the "fanservice" was mainly intended to show the terrible situations that different characters are put into. It's hard to explain without spoiling the show, but around half of the "fanservice" in this show isn't your usual sort of fanservice in that it is not supposed to please fans (unless we're talking about disturbing psychopathic ones), but rather to make people sympathize with the characters.
As for the gore,thankfully, most of it was not really animated in great detail, and usually the gore is just there to be an additional tearjerker or shock factor.
TL;DR: Elfen Lied has no plot, has no real characters, has mediocre voice acting, and a LOT of (sort of?) fanservice and (poorly animated) gore. These are all the weak points of the show. Look past these numerous flaws, however, and you will find an incredible emotional rollercoaster that plays with your heartstrings like a cat with a mouse.
