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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.
In recent years, there have been many Role Playing Games that incorporate dating sim elements. These dating sim elements are often referred to as Romance Sidequests in the RPG genre.
Agarest Senki - where the level of affection between the protagonist and the chosen heroine will affect the outcome of the next generation protagonist.
Il Palazzo, 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 Cannot 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 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.
La-Mulana, upon acquiring certain MSX ROMs, lets you play what at first appears to be an MSX knockoff 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.
Date A Live plays this straight with the twist that the protagonist doesn't make the decision making part. Rather, it's his sister and the Ratatoskr crew aboard the Fraxinus who makes the decision making part.
Oddly enough, Grand Theft Auto 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, and 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 to. Each girl also has a totally different personality and interest, along with benefits if they like you enough — dating the lawyer Kiki, for instance, will allow you to get out of a wanted level of up to three stars.
A similar system is even used with some of the male characters. Although their activities are strictly of the guy friend variety, like drinking or going to a strip club, it's still the same basic feature, and you can get similar bonuses from being friends with them — your cousin Roman offers free cab rides, Little Jacob offers discounted weapons, etc. They also implement this feature directly into the storyline several times; you have two canonical girlfriends over the course of the game, while the ending you choose results in the death of either your dear cousin or your already mentally scarred girlfriend.
Grand Theft Auto: San Andreas also had this feature, albeit a stripped down earlier version. It doesn't tie too much into the story aside from stealing an access card from one of your girlfriends, though you do receive rewards like special outfits and access to their cars.
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.
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).
The awkward dialogue of Festival Days must be seen to be believed.
The happiness level in some versions of Pokémon has more than a shade of this, with your Pokémon reacting well to "gifts" like Potions and Stat Ups and badly to failures in your cooperative battles.
Sleeping Dogs reportedly has something similar to GTA IV with 4 women to date that offer a bonus once your relationship is good enough. In-game, though, it amounted to one side-mission per girl and collectables showing up on your map.
The Dawnguard DLC for The Elder Scrolls V: Skyrim has shades of this in the form of Serana. Throughout the questline, when her past and lineage are slowly revealed, you can be polite and understanding in your dialogue, or you can be forceful and rude. While you can't marry her, if you're polite enough, you can convince her to cure herself of vampirism if you ally with the Dawnguard.
Mount & Blade is mainly a Strategy RPG, but it does have a rather complex courtship system that allows you to woo and possibly marry various ladies. Each lady has a certain personality that affects her opinion on certain matters (your character's Honor and Renown, tournament dedication, various bits of poetry you can recite, etc.). Of course, since the game takes place in a medieval setting, there's more to it than just winning her favor most of the time...