If you liked the Welcome to the NHK! anime, the Anime-Planet community thinks you'd like:
After having lived elsewhere for several years, Sana returns to the town in which he grew up in, and quickly begins to reacquaint himself to his surroundings and new high school. While there, Sana runs into his four childhood friends: Shuu, Shuri, Aoi, and Nanaka; but for some strange reason Nanaka gives him the cold shoulder. As he goes about his new daily life, can Sana rebuild his friendship with Nanaka while trying to deal with a troubling secret from his past?
A tentative recommendation, however both are dramas that deal with the themes of suicide, and responsibilities to parents/work... Myself, Yourself is more heavily romance and doesnt have the humour, nor is it as 'complex' as NHK.
In the future, a devastating event known as Second Impact has destroyed Tokyo as we know it, giving rise to Tokyo III - a city under siege by mysterious lifeforms known only as Angels. Mankind's only line of defense are the Evangelions, a set man-made machines piloted by a trio of fourteen year-old teenagers, Rei, Shinji, and Asuka. The fate of Japan and the entire world now lie with these three children, though they might not have the power to save the most important thing of all: each other.
In both series, all the characters have huge mental problems and most of the plot is about getting over them. Welcome to the NHK is a little less subtle about this, given its comedic value, but I think it would still translate well.
The studious and uptight Chiaki is well-known as the top pianist of his school, and dreams of becoming a world-class conductor like his idol, Viera; but his fear of flying (which makes studying abroad impossible) combined with a recent break-up and dismissal from his piano instructor causes that future to seem both bleak and unlikely. After collapsing outside of his apartment, drunk, Chiaki inadvertently meets a young woman named Nodame who, while quite talented at the piano, is unclean, clumsy, and haphazard. Despite being almost polar opposites, the two begin to grow closer and work, together, to overcome the obstacles in their careers.
Nodame Cantabile and Welcome to the NHK! are exciting roller-coaster comedies about the developing relationship between two character archetypes: a cool, standoffish guy with big dreams; and an upbeat, quirky girl with a painful past. This fateful relationship eventually leads to the odd couples' bring out the best in each other and overcoming of their personal weaknesses. Even though Nodame is very light-hearted and NHK is distinctively darker, the two are comparable in its use of characterization more than slapstick to achieve laughs. Both shows are delightful and even surprisingly moving when dealing with the couple's relationship.
Ouran High is a school for the extremely wealthy or, in Haruhi's case, the extremely talented. But no amount of talent will help when Haruhi accidentally drops an eight million yen vase in a music room. The vase was the property of Ouran High School Host Club, a group of attractive young men who, for a fee, provide their time and affections for their lovesick clientele: the female students. Fascinated by this strange new specimen, a poor and clumsy commoner, they force Haruhi to work for them until the debt is repaid; but they get a lot more than they bargained for...
Just like NHK's occasionally paranoid Sato, Ouran's male lead, the charming Tamaki Suoh, often has moments in the series when his imagination is kicked into overdrive and causes him to spazz out. If you like characters with runaway imaginations, then watch Ouran High School Host Club.
Takao Kasuga is a lonely boy who spends his days immersed in books to escape his frustration with life. His only source of joy is the beautiful Saeki, who he secretly admires from afar. However, Takao's obsession goes too far one day when, in a moment of emotional folly, he steals the girl's gym clothes and takes them home with him. Worse, his terrible deed is spotted by Sawa Nakamura, a mysterious outcast who sits behind him in class who threatens to reveal the boy's secret unless he promises to engage in a contract with her. At first it seems Sawa just wants some companionship, but soon it becomes clear that this "contract" involves more than mere afternoon chats. In fact, Takao is about to discover just how dangerous his bond with Sawa is and how it threatens to tear everything - his life, his love, and even his sanity - apart.
As soon as I started watching Flowers of Evil, it reminded me of Welcome to the NHK! Flowers Of Evil is slower paced, and doesn't have as much comedy as Welcome to the NHK!, but the main character in both series, with their dysfunctions and twisted relationships with the women in their lives, are pretty similar. In particular, there's parts of both Nakimura and Saiki (Flowers of Evil) in Misaki (Welcome to the NHK!), both in terms of her actual personality and in terms of how Satou reacts to her.
In general, both of these series are about characters on the fringe of society that feel trapped and lonely, and about damaged people that seek each other out (whether or not the relationship they have with each other is actually healthy). And they both feel a little removed from the typical anime series, with slower pacing and a story that actively defies escapism.
I absolutely think that fans of one have a high chance of liking the other. If you like one, I totally recommend the other.