Ah! My Goddess can be considered a precursor to the harem genre, even predating Tenchi Muyo!. It involves lovable loser Keiichi Morisato dialing a wrong number and accidentally calling a goddess to his apartment. Thinking it's a joke, he wishes for her to stay with him forever (not that he's averse to that). Over time, Belldandy's sisters Urd and Skuld move in, too, with other female characters joining in at various points. That said, while several of the other women tease Keiichi at times, he only has eyes for Belldandy.
Ai Kora (from the creator of Midori Days) plays with this: Hachibe Maeda, a guy with very particular tastes in women definitely wants the harem so long as they have exactly one of the attributes he's looking for in a girl: Tsubame-sensei, the Harem Nanny, has long, streamlined legs; Sakurako, the Tsundere, has big, blue eyes; Yukari, the Meganekko, has big, perky breasts like a bullet train; and Kirino, the Little Miss Snarker, has a husky voice. Later we meet Ayame, the Ojou, who has Maeda's ideal waist. This is taken to the extreme with Haiji, who has the ideal ass but is a guy. And a bisexual, no less.
Nadja Applefield (or better said, Nadja Preminger), from Ashita no Nadja is another of the female examples, having one of these (with four pre-teen boys and three guys in their mid-to-late teens) when she's just thirteen.
Spiritual SuccessorBrynhildr in the Darkness is a better example than Elfen Lied. Like in Kohta's case, a lot more girls are living in Ryouta's club house, since they are all refugees from Vingulf, a laboratory that creates Magicians. At least three of them have fallen in love with him, with Kuroha turning out to be his Childhood Friend Kuroneko, who was believed to be dead, is the one he truly loves, but several incidents force them to be Star-Crossed Lovers. The only girls who aren't in love with him are Kana and Kotori. Meta-wise, Die for Our Ship is avoided by the fans, since death is very possible in this series, as Kotori dies in the climax of the first part of the series, and Nanami died before even joining the main cast.
Chivalry of a Failed Knight: Completely averted. At the beginning it seems that this will be your typical harem series, seeing how the Light Novel seems to be playing the tropes straight, but by the end of volume 1 (chapter 10 in the Manga and episode 4 of the Anime) both leads Ikki Kurogane and Stella Vermillion become an Official Couple. The series also subverts many common tropes from harem series, where the leads solve their differences rather quickly without pading the drama, instead focusing on progressing the romantic relationship.
Code Geass: It seems like everyone in the series is in love with Lelouch(whowouldn'tbe?). In the first season, Lelouch/Zero accumulates a rather large group of both genders who have feelings for him, including Kallen, Shirley, Euphemia, Kaguya, Suzaku, and Rolo. He just doesn't do anything about it, since for the most part he's too busy trying to overthrow the government to pursue romance. The second season seems to poke fun at this; as a result of his Ninja Maid running around in a Lelouch disguise and being generally nicer, Lelouch ends up scheduled to go on dates with no less than 108 girls. And there's Kaguya fantasizing about polyamory…
This was parodied in one of the first season's audio dramas where Shirley considers asking him to go to a concert with her and imagines him revealing that he was in love with and getting married to Kallen, Nunnally, Suzaku, Milly, Rivalz, and even Arthur the cat in that order. At the end they all decide to share him and invite Shirley in on the action. Note that Nina was not in the fantasy and it was set only hours before the Table-Kun incident.
Date A Live: Shido Itsuka must become a Chick Magnetby necessity to save the world. The series involves him dating Spirits, getting them to fall in love with him and sealing their powers with a kiss so they can live normal lives.
El Hazard: The Alternative World. The original El-Hazard series had a few characters somewhat interested in the male lead, but it was tapped for occasional fanservice and comedy rather than being the focus. However, the third OVA dove straight into this genre by having three girls fight over the (taken) main character in every episode. This is one of the reasons that it's seen as inferior to the first two.
Gender-inverted with Fushigi Yugi and its protagonist Miaka, with the added bonus of some minor overlap with a traditional Royal Harem.
Girls Bravo centers around Yukinari, who suffers from an allergic reaction to girls after being bullied by them for years. Enter Miharu: a strange girl from another planet, who falls in love with him at first sight and is the only one who doesn't trigger his allergy. There's two other girls for her to compete with… except not really.
Hayate the Combat Butler, a strange combination of the guy being even more clueless than usual and the girls mostly being knowledgeable about and completely alright with competing for his affection between them. Several of them actually work very hard to get one of the other girls to win!
Tomoki Sakurai from Heaven's Lost Property has a harem consisting of Ikaros (who still hasn't quite realised it), Nymph, Sohara, Hiyori, and possibly Astraea. However, he's way too busy thinking of perverted schemes and being a pervert to actually notice. Only Hiyori has confessed to him, and he's even stunned upon receiving her confession.
High School D×D with the added twist that every girl in the harem is willing to share, but they're competing to see who's first place.
According to a non-canon pre-anime Drama CD, this happens in Higurashi: When They Cry. After Keiichi goes even more bishonen than he already is, it's shown that Rena, Mion, Rika and Satoko all like him.
There is also a Kira episode that's a better example, with Shion, Rena, and Mion all out for Keiichi.
Holy Corpse Rising: To win a desperate war against evil witches, Nikola Eskalibur manages to bring members of the "First Witches", who are not aligned with the evil witches, back to life and convince them to help him seek out and destroy the evil witches. What he didn't count on is by the ancient laws, bringing back a First Witch counts as marrying her. Soon he has several incredibly powerful girls fighting over who gets to be top wife.
Infinite Stratos somewhat induces this by necessity: There's the eponymous Powered Armor that only girls can use, but for some reason, one guy is able to use it as well. He gets plunked in to a dedicated all-girls school to learn how to use the same.
Kämpfer: Here the main guy turns into a girl thanks to a magical MacGuffin. Who's probably hotter than the rest of the main girls. Problem is that the girl he loves is 100% lesbian and the Big Bad of the series.
Can't forget the lesbian Love Triangle in Kashimashi: Girl Meets Girl from which Hazumu has to choose either Yasuna or Tomari. In addition to that loads of other characters be they guys, girls, aliens, or family members all have a thing for Hazumu.
Maou no Hajimekata offers a somewhat dark take on the genre, the resident Villain Protagonist Aur is fond of recruiting many women to his cause, some come willingly as they don’t like humans as well or don’t mind Aur’s misanthropic tirade against them, the good natured women however are met with several doses of brainwashing through sexual assault till they start liking Aur and become fully supportive of his deeds.
My Monster Secret: Starts off looking like this, but is ultimately averted. While Asahi does have multiple girls interested in him, from the very beginning he's only got eyes for Youko. The girls are all friends and they all gladly support the couple while trying to get over their own feelings for Asahi, which tend to fail for the sake of comedy (which is just as much a part of the story as the romance). In fact, the series doesn't just avoid Fanservice, it takes great delight in mocking the concept repeatedly; for example, despite being quite attractive Youko couldn't seduce her way out of a paper bag, and her idea of "sexy poses" makes her look like a reject from a Super Sentai team.
Omujo! Omutsu Joshi would be just another ecchi harem manga with plenty of panty shots and occasional suggestive situations were it not for one additional quirk: The three girls of the harem, be it for personal need, personal pleasure, or the personal belief it's what the male lead is into, all wear diapers.
Played with in the manga Otomari Honey, where we see the situation from the perspective of one of the haremettes — she goes to the house of a boy she has a crush on to ask if she can live with him to get away from her own home, only to find that he's already got three other girls with the same story living in his room.
Ranma ½: Akane is an inverted example while Ranma has two — one as a male and one as a female.
Rosario + Vampire. Tsukune falls in love with Moka, who has also a superpowered neutral true side. Other girls fall eventually in love with him, with Yukari routing for a One True Threesome, Ruby having a minor crush in comparison to the other girls, and Kurumu and Mizore also having species problems. Kurumu would literally die if Tsukune rejects her, and Mizore's species is endangered, so she needs to mate with him. Fang-Fang is the Gay Option, who just wants to Tsukune to join his mafia family rather than because of romantical reasons, but Fang-Fang offers him the Marry Them All option, which would make every girl but Moka happy. And Kokoa has no interest in Tsukune at all. To make it more complicated, while Tsukune has only eyes for Moka, there is the Outer Moka-Inner Moka problem, since the girl he first fall in love is Outer Moka, but he has also feelings for Inner Moka, so the best option is that they somehow emerge together. Both Mokas are in love with him, but they also help each other. Even more confusing, it turns out that Outer Moka is a clone of Moka's mother Akasha. However, the personality of the deceased Outer Moka does merge with Inner Moka's.
Saber Marionette J, in which the entire harem is made up of Robot Girls and one guy (on an all-male world, where this would be expected). In its various sequels, the one real girl in the entire world also apparently wants in on the harem.
Seitokai no Ichizon. The male lead blatantly announces he is aiming for one to his female cast more than once. He's generally a nice and dependable guy and, in a way, it pays off by the end.
Sekirei: The main character gets his harem by "Winging" the girls, meaning as he kisses them, they get wings. He's not the only one, and women are not the only ones who can get winged, but he's the main focus.
Shitsurakuen gives us an example. Unusual in that the harem and the one seeking it are both female.
SHUFFLE! sets up a contest of sorts for the lead's heart. There's remarkably little hostility between the competitors.
Sister Princess: An interesting (and unusually non-romantic) variation on this trope can be found in the anime. In which, a young man discovers that he has a baker's dozen half-sisters he never knew existed. Having grown up alone except for a few servants, he finds their slavish adoration of their "big brother" somewhat overwhelming, but grows to love and treasure them all.
So, I Can't Play H! begins with Ryosuke's neighbor, Mina, already nursing an unrequited crush on him since childhood. But the first episode's opening scene introduces his soon-to-be love interest: a stunning redhead named, Lisara, whose not only a shinigami, but high-ranking nobility. Then the other two shinigami show up (Quele and Ilia) and Mina's chances effectively go down the drain.
Strawberry 100%: Manaka has a rather large group of different girls after him in Aya, Satsuki, Tsukasa, Kozue, and Yui.
The World God Only Knows is a rare example of the lead character working for his harem, but he's only doing it because he has an Explosive Leash forcing him to. And technically the harem doesn't really exist since the girls are given Laser-Guided Amnesia after the conquest is over. It gets played more straight later on when some of the girls recover their memories, but it isn't the girls who get to fight over him, it's the goddesses they are hosting.
The To Love-Ru sequel, To Love Ru Darkness has the rare Harem Seeker… who isn't the male lead. Momo, one of the girls in Rito's Harem, wants to create the harem for him, with her in it, and pretty much every other female he has ever met.
Urusei Yatsura shows how this was already a cliche back in the 1980s — Ataru Moroboshi, who is actively trying to assemble a harem, repulses most girls and has to "settle" for the alien princess Lum, who lives in his closet and thinks they're married.
World's End Harem: After 4 years in cyostasis to cure him of his terminal disease Reito Mizuhara awakens to see that society as he knew has completely collapsed, during his cold sleep a new virus surfaced and wiped men out of the face of earth, save him and four other males, now the surviving women struggle to maintain what was left of modern society and urges Reito to become their breeding stallion.