The Dating Sim is a type of game designed to set up goals, usually in the forms of schedules and stats corresponding to social skills, which must be achieved to discover a story focused entirely around the Character Development of the player's chosen girl/guy, get into his/her pants, or both. This leads to Multiple Endings, though some Dating Sims make it possible to see several of these "endings" in a single playthrough.
Some Dating Sims have been made into harem anime, though the result is usually nothing special due to the removal of sex and the fact that the narrative can no longer focus on any single character.
Because there is almost no market for true Dating Sim games outside of Japan, it's a frequent misunderstanding among western gamers that "Dating Sim" is the general term for all ren'ai (romantic love) games. In fact, many romance games are Visual Novels, which is a much different game style. (See for example, the difference between the Ace Attorney series, which is very close to a Visual Novel style of gameplay, and the DOA Xtreme series, which is the closest thing to a true Dating Sim with mass-market appeal in the US.) If the game plays out like a Choose Your Own Adventure, that's a Visual Novel. If it feels like you're playing an RPG, trying to keep track of everyone's feelings about you and giving out presents, that's a Dating Sim.
Examples
Agarest Senki - where the level of affection between the protagonist and the chosen heroine will affect the outcome of the next generation protagonist.
Getter Love!! (the * only* dating sim on the Nintendo 64.)
Graduation, probably the first officially-translated (though localized from the original Sotsugyou 2 ~Neo Generation~ which was Tokyopop was before it became Tokyopop).
Jewelry Master Twinkle has elements of this. It's mainly a Falling Block Game, but at the same time, you have a girl talking to you. Depending on your performance, you will get different dialogue branches; at each fork, you can either get a good branch (green background) where you're winning her affection, an okay branch (blue background) where you're getting along okay, and a bad branch (red background) where you're turning her off. Do well enough and she'll change costume at the end, and unlock a new date where she gets a little more personal with you.
Persona 3 is half Dating Sim with the Social Link system, half dungeon crawler RPG (where the state of your Social Links helps determine which personae you can use and how much XP a persona gets when it's first fused.) Same with...
Persona 4, which also adds special techniques for your party members (such as taking a fatal hit for the protagonist or straight up kicking an enemy out of the fight) depending on how high their Social Link ranking is.
You became friends with Yosuke. Yosuke will now DIE FOR YOU.
Sprung: A dating simulation released in English for the Nintendo DS in 2004, with a PG-13 level of content. It received poor reviews. During the lifespan of the DS, it often appeared in bargain bins and used game shelves.
Star Ocean: A series of Eastern RPGs that include a relationship-building system similar to Dating Sims, including the use of Relationship Values, leading to dozens of possible Multiple Endings for each game depending on how strong the relationships are between the various characters.
Summer Session: A dating simulation with a PG-13 level of content, originally written in English, and released in 2008.
This is an interesting series as the games vary in genre. The main entries in the series are SRPG's whereas the other games in the series are action games. However all of them incorporate Dating Sim elements with the standard multiple endings for the characters that join you.
Surviving High School: A dating simulation with a PG level of content, and mini-games. Originally written in English. It was first released on cellphones, and later released for iPod Touch / iPhone and DSiWare.
Tokimeki Memorial was one of the first hugely popular and successful games in the category, paving the way for everything that came after.
However, no games in the franchise were officially translated outside of east Asia. Only the Nintendo DS versions of the first two Tokimeki Memorial Girl's Side games have received unofficial localizations.
This is exactly like the Summon Night series with the main difference being that virtually all of the games in this series are SRPG's but like Summon Night they incorporate Dating Sim elements with the standard multiple endings for all the characters that join you, in addition to some of the supporting characters.
Virtually Date Ariane (One of several virtual date Web Games, created by English speaking designers, with polygon graphics. It emphasizes moment-by-moment gameplay rather than story. Its content is Not Safe for Work, and the 3D graphics fall into the Uncanny Valley, especially during close-ups.)
X-Note (Zeiva Inc's second commercial game, with a fairly bleak story about psychic powers and unsolved mysteries.)
Excel Saga, naturally, did an episode parodying these. In a Running Gag, the male characters suddenly find themselves in a game with several options, the last generally being "Put It In."
Ilpalazzo, playing the game, gets a bad ending by killing the Patient Childhood Love Interest who wakes him up in the game, before even leaving for school.
In the last two episodes, Watanabe gets the dating sim option popup when he encounters Hyatt. (He almost gets the good ending, too, but Excel interrupts.)
Likewise, one episode of Abenobashi Mahou Shoutengai featured a world that partially functioned as a Dating Sim (with an all-girl cast and drawn in a Moe style), to the point of Sasshi requesting a replay so he could end up with a different girl.
Galaxy Angel (ONLY the games; the anime is something altogether different)
Super Paper Mario parodies the genre in a pre-Boss Battle cutscene. When the boss, a geeky chameleon named Francis, meets Princess Peach, the game turns into a dating sim with Francis playing it and the player providing her responses. Princess Peach quickly becomes annoyed at the concept, and sics Boomer on the Nerr2Babe Interface - which has the side effect of nuking Francis' video card. Cue the boss battle, folks.
To both reiterate and answer the Excel Saga quote, Peach indeed had a bomb available.
Final Fantasy VII has an ongoing pastiche of one, which leads to dating one of four characters (one of which is The Lancer and extremely male) at a minor scene later on. Interestingly, all of them contain some character and plot development - Aerith's scene foreshadows Cloud's Tomato in the Mirror moment later on, Tifa's serves as proof that she Can Not Spit It Out, Yuffie's is the only one in which Cloud actually gets a kiss, and Barret's is part non-sequitur rant, part self-parodying Ho Yay, and culminates in Cloud being (bizarrely) accused of being a paedophile. Cloud's relationships with other characters also affect several other scenes, including one near the end of the game that may imply a sexual encounter with Tifa if her Relationship Values with Cloud are high enough.
In Genshiken, shameless Otaku Madarame spends almost a whole episode in a room alone with Dungeon Masters Girlfriend Saki, trying to work up the courage to talk to her. This is emphasised by dream sequences in which he imagines her as a character in a Dating Sim, complete with Art Shift - and repeatedly ends up clicking 'Do nothing'. He bemoans in his internal monologue how real life has more choices than just three, and how it's not always obvious which one to make.
In Axis Powers Hetalia, Korea asks if China likes him. China is about to respond with no, but stops when he sees a little box above Korea that says that any response will lead to sex. Which is somewhat awkward considering the two are brothers.
In Full Metal Panic!, Sousuke's classmates attempt to prepare him for a date by having him play a Dating Sim. His military-wired mind causes him to be blatantly honest to the girl, upsetting her and losing the game, much to his consternation.
A similar arc occurs with Vanilla in Galaxy Angel.
La-Mulana, upon acquiring certain MSX ROMs, lets you play what at first appears to be an MSX version of Tokimeki Memorial, and the heroine, Shiori, is talking about how she'd like to take her friendship with Taihei (your character) to the next level until she comments that she had a toothache since this morning. Taihei then discovers a piece of fake skin on the ground, and Shiori then reveals herself to be aSnatcher. After satrical dialogue on women in dating sims, you're thrown into a battle against Shiori while being careful not to shoot the "game mascot", Gyonin (A.K.A. Metal Fish MSX3 Turbo R Plus). After the whole ordeal is over, another girl named Nijino runs up... only to reveal herself as a Snatcher as well. And the whole thing starts all Syntax error in 1220
Seto no Hanayome has an episode where San's Dad, Lunar's Dad, Shark Fujishiro, and Masa played one of these games in an attempt to understand girls' feelings so they can better relate to San and Lunar. It ends up failing in an epic fashion.
Done as a joke at a comicon in Japan, where Studio Pierrot showed a redubbed set of Bleach clips meant to be an advertisement for an upcoming dating sim.
There's two 'dates' in Metal Gear Solid: Peace Walker, where you can go to the beach with either Paz or Kaz. You speak to them using the Co-Op battle cries, and then (if they like you) you can invite them into the cardboard box for quality time. They're parody, but both Paz and Kaz have different personalities which come out during the dates (Paz likes being complimented and treated gently, Kaz likes being punched and Big Boss staring at his crotch with the binoculars). Hilariously, you have to successfully seduce both to get the 100% Completion conversation.
In the Strong Bad email date, Strong Bad creates the “Homestar Runner and Marzipan Extra Real Dating Sim XR” to simulate what he imagines what Homestar and Marzipan actually do on a date.
A Yuria 100 Shiki omake features the Yuria 100 Shiki eroge. The first options all immediately lead to a sex scene except for the youngest female character, which immediately leads to the player getting arrested as a pedophile.
The Journal ComicDoodle Diaries featured a short parody of dating sims, starring the three main characters as the love interests.
Special Mentions
Oddly enough, GTA IV has this as a feature, complete with different places to go, activities to play, and different opinions with each and every girl. You can even meet them online on the internet and eventually have "hot coffee" with them. Your clothes, vehicle, driving skills, calling time, amount of calling (if you call too much, you're a stalker, but too little, and they'd think you'd forgotten them), all count in to how they view you. They remember what you have and where you go too. Each girl also has a totally different personality and interest, along with benefits if they like you enough. Even more surprisingly, you can also hook up with guys, although they are of the guy friend variety, like drinking or going to a strip club, but it's still the same basic feature. With all this, they also implement this feature directly into the storyline several times, along with the horrify ending with deciding the death of a dear friend or already mentally scarred girlfriend.
San Andreas also had this feature (a stripped down earlier version), although it didn't tie too much into the story aside from stealing a access card from one.
The main point of these friends is to make the player's life easier: free transportation, Get Out Of Jail Free, guns, cars, lower wanted level...
Flash games: a number of English-speaking fans have created stat-driven dating simulations using Flash. The "sim date" games emphasize gameplay over story or characterization. There are a number of games which use original characters and settings, both for male and female audiences. Others are based on popular series, such as Naruto. (Unfortunately, the sim date games based on Evangelion, Love Hina, Azumanga Daioh, and the Galaxy Angel anime use out-of-characterswearing instead of characterization.)
Mass Effect 2: Legion, a robot, purchased a dating sim based on a blockbuster romance film between two different aliens. His score is 15 (hopeless), humorously contrasted with the rest of his game scores (that consist of a million sniper kills on a generic FPS, et cetera).
Actually, the Mass Effect series also has some dating sim components itself. It's secondary to the general RPG and third-person shooter aspects of the game, but you actually can build relationships with various characters through dialogue choices (and some of these can become romantic), so I think it qualifies.