Harem is a genre/plot frame that is mostly present in the Japanese media of Anime, Manga, Light Novels, Visual Novels, and Video Games.
It normally takes place in a High School setting, with one male lead, and at least three, often a lot more girls, who are romantically interested in him. ( Gender Inverted Examples also exist). Usually, each girl personifies a single classic characterization archetype.
The protagonist either takes it as an Unwanted Harem, or reacts as a Harem Seeker, or Oblivious to Love.
Works where a Harem Genre set-up is put in front of other relationship dynamics, and the plot is written with the intention to keep the "race" for the male protagonist's heart as tied as possible, are known as the Balanced Harem subgenre. If it is reversed it is known as Cast Full of Pretty Boys.
In other cases, when a work uses this genre together with a more traditional Romantic ComedyOfficial Couple relationship, that is called the Supporting Harem subgenre.
Many of these works are also shared with the Ecchi genre, as it is harder to find a Harem story that isn't filled with gratuitous Fanservice than one that is.
Code Geass: It seems like everyone in the series is in love with Lelouch. In the first season, Lelouch/Zero accumulates a rather large group of girls who have feelings for him, including C.C., Kallen, Shirley, Milly, Kaguya, and even his half-sister Euphemia. 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 staff has said that the second season will deal more with his romantic entanglements (and note that all this is ignoring the Brother-Sister Incest and Ho Yay-slash-Foe Yay ships with Nunnally and Suzaku, respectively, and a combination of both those tropes (though a downplayed one that doesn't get as much focus) with Schneizel, who refers to Lelouch as the "one he loved and feared the most").
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 a Tenchi Solution...
And yes, the staff sort-of delivered it. Not only Rolo became a secondGay Option (who was all "Bitch, PLEASE!" at Sayoko for the 108 dates), but there is more focus on Lelouch's love life... Specially when it hit Fatal Attractor levels and later Suzaku manages to ensnare the position of The Dragon to Lelouch, with all the Ho Yay squeals it implies. See the entry.
This was played with 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.
Infinite Stratos: Slight variance on it in that there's some Powered Armor that only girls can use, but for some reason, one guy is able to use it as well, and they promptly put him in the all girls school to learn how to use those things. Naturally, being the only guy in an all girl school...note that it was played up in the anime. In the light novels, its just a few harem elements here and there, but in the anime its a standard harem series with a Powered Armor twist.
Kampfer: Here the main guy turns into a girl thanks to a magical MacGuffin. Who's probably hotter than the rest of the main girls. Like Infinite Stratos, above, the anime is a much more traditional harem series than the original novels.
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!
RPG Shooter: Starwish is a hybrid RPG shooter where the harem consists of 4 girls (not a Four Girl Ensemble since only 3 are available at a time) and 2 guys, with a special ending if you can get all of the individual endings (and another one - featuring a fifth girl who was not previously in the story except for a few lines at the beginning, which the protagonist assumed was All Just a Dream - if you don't).
Ar tonelico series is a RPG hybrid with Visual Novel element in the form of Cosmos Sphere, focusing on romance developments between The Hero and two (later three) heroines. Ensemble Darkhorse Cocona not included.
In Bully, the main character amasses himself a nice harem.
In Scarface: The World is Yours Tony Montana can obtain a large collection of trophy girlfriends.
Agarest Senki requires you to pick one girl out of three in each generation after you've spent some time with them. The system works similarly to Phantasy Star III's syetem. Rex, the final hero, however, can end up with one of any girl you've gotten in your party so far of the maximum number of nine in the Golden Ending.
Other
In the Book of Genesis, Jacob agrees to work for 7 years in order to marry Rachel but on the night they are supposed to consummate the union, Rachel's father Laban sends his older daughter Leah instead. Jacob "knows" Leah and therefore has to work for another 7 years in order to marry Rachel. After Leah knocks out 4 kids, Rachel becomes jealous because she has yet to become pregnant and offers her slave-girl Bilhah to be impregnated instead. She knocks out another 2 kids. Now Leah becomes jealous and offers her slave-girl Zilpah to Jacob as well. She knocks out two more kids. Then Leah's oldest son Reuben gives his mom some flowers, which Rachel sees and demands Leah give some to her as well. So they make a deal where Leah gives Rachel some of the flowers in exchange for a night with Jacob. Leah then has another 3 kids. Finally, after all this, Rachel gets pregnant and has a son.
Works that are harem, but subvert, deconstruct, or otherwise skew the genre away from normal.
Anime and Manga
Rosario + Vampire starts out a normal Supporting Harem (and in many ways, still is one) with an Unlucky Everydude protagonist stuck in a school for monsters, but slowly adds darker elements, as well as more shounen-action style plots. Now the main character is a bishonen badass who probably doesn't count as human by most measures.
Mahou Sensei Negima! is...complicated. It was written by the same author as Love Hina, who wanted to do a shounen-action series from the start. His publishers insisted on a standard harem series, which he pretended to do. The main character is a ten-year old male wizard teacher at an all-girls school, and his 31 students aren't interested in him romantically, but rather because they think he's the cutest thing since Hello Kitty. But as the series progresses, he becomes such an uber-badass that they all eventually fall in love with him anyway.
The World God Only Knows is a reconstruction of the harem genre viewed through the lens of eroges. The protagonist is forced to make girls fall in love with him due to an Explosive Leash, despite the fact that he hates real girls. In the process, the series tears apart all the stock characters, shows how they're not realistic and then puts them back together again with an overall attitude of 'No, it's not realistic at all, but that's okay. Isn't it better like that? Even with those stock characters, can't the story still be meaningful?'
