In Turgor If you open Sister's hearts, they will allow you to go in their chambers and travel to other sisters. It is also implied that the chambers of a happy Sister give more Color. However it is heavily subverted when you find out that giving Color to a Sister heavily damages their realm due to the sheer amount of it you need to use, which will actually decrease the amount of Color you can get. This will eventually lead to the Scorpio appearing, which will completely destroy your gardens.
Hack And Slash
If you marry someone in Dynasty Warriors 6: Empires, you can "rest" with your spouse, which levels you up.
Firan MUX has recently inputted a system where you get a temporary buff to your stats if you sleep with a whore while stationed at the front during war season.
La Tale has a marriage system, where a fully intimate couple gets a 10% boost to their main stats, and with some special items give access to unique skills like summoning your partner, a full heal, and an experience boost.
In Ragnarok Online the Alchemist job can create an Homunculus, a fighting pet which has an "Intimacy" indicator. Once it gets past a certain level, the Homunculus can be evolved and gains access to a powerful skill.
Married characters gain unique abilities that work exclusively on their partner. Couples may also adopt a child character which unlocks similar abilities.
Real Time Strategy
In the Galaxy Angelgame verse, your relationships with the Angels makes them stronger, and inversely, they like you more the better they do in battle. Insulting them makes their stats drop, and if you let them get blown up, they hate you.
Nethack players can receive substantial good or bad effects from sleeping with succubi or incubi, but with proper preparation they'll almost always be positive. This includes permanent stat gains and instant level ups, and if you have a method of generating many such demons can be used to vastly inflate your max hit points even after you reach level 30.
Dwarf Fortress is a partial example. Dwarves gain skills by hanging out with friends and lovers, and skill boosts will arbitrarily make dwarves stronger (even though this makes no sense for social skills). Thus, that dwarf that slouches in your dining room all day partying and making friends with everyone could very well be more dangerous than your elite military.
That is, untill one of the said friends die. At that point, kiss your fortress goodbye when your elite dwarf goes berserk...
...and kills other dwarves, which, of course will cause OTHER loved ones that go berserk over their deaths, which causes MORE death, which in turn causes MORE madness, and so on in a descending spiral of blood, vomit, and carp...
...and magma. It's not truly a tantrum spiral of doom until someone accidentally floods the entire fort with magma.
Mostly averted now, since skills only raise related attributes, but you still get such gems as fishing, studying, medic skills, and book keeping improving a dwarf's accuracy with a crossbow and Intimidation and Comedy letting a dwarf run faster.
Which makes sense. A high Comedy skill improving speed clearly makes the Dwarf a Running Gag.
Role Playing Game
Shin Megami Tensei: Persona 3 is a definite example - the various Persona you can use grow stronger as you strengthen your relationship with the character who is associated with the same Tarot Motifs. In the case of female characters, that relationship tends to be romantic in nature. In order to create the Ultimate Incarnation of each Tarot, you need to max out your relationship with that person - of course, that also means that if you want a good lineup, your character is going to turn into a real Casanova, since he'll have to win the hearts of five different girls in the same school...
AND you win the affections of 2 girls who you can't actually have a relationship with (a preteen girl who promises to marry you when she's older and your female homeroom teacher who you meet anonymously through an online game). And in Persona 3 FES you can sleep with Elizabeth, although she's not a social link. Talk about the living incarnation of studliness...
Persona 3 Portable adds in a female protagonist, who can choose out of 5 options (Akihiko, Shinjiro, Ken, Ryoji and Theo) along with crushes from Bebe and Hidetoshi. She can choose at specific points if she wants to date someone, ala Persona 4. And for the guy, there's no consequence for dating multiple girls, ala Persona 4.
Persona 4 continues the trend but applies it to your allies. Odd-numbered Social Link ranks add additional in-battle effects ranging from using follow-up attacks to taking lethal attacks for the MC, while the Personas of your allies will only mutate to their final forms once you have fully maximised that person's Social Link. In that game you don't have to raise the females' Social links romantically (thus you can remain faithful to one girl); though choosing the romantic route will show different scenes.
Devil Survivor 2, another Shin Megami Tensei spinoff, features the Fate System, which works similarly to the aforementioned Social Links: reaching ranks 1, 2 and 4 bestows additional benefits to the character in battle, while ranks 3 and 5 unlock new demons for fusion. In addition, there's a point in the game at which all but a few of your allies leave you—which ones stay depend on your route. While there's no route that allows you to recruit everyone (the Anguished One is only available on his own route, where neither Yamato nor Ronaldo can be recruited, and you can't recruit either Ronaldo or Yamato on the other one's route), you can't rerecruit anyone who you have rank 3 or lower with.
Thousand Arms combines RPG gameplay with Dating Sim aspects. The more the girls like you, the stronger you get!
Neverwinter Nights 2 Mask of The Betrayer goes and makes the only romance in a BioWare/Obsidian title that would be unforced give you a feat for finishing it (The male PC romance plot also gives a feat, but it still has the other issues).
The non-romantic relationships also give bonuses. For example, maxing out the bear Okku's respect for you causes the Hunger Gauge to deplete much more slowly.
In Baldur's Gate II: Shadows of Amn, romancing Jaheira the "right" way gets her a Harper Pin, which grants several useful bonuses. While better replacements show up near the end of the game it's a good item for most of the mid-game. More importantly, however, successful navigation of this quest (which is not actually part of the romance, but gets powered up if you're in a romance with her and weaves in and out of it), nets you a few large buckets of experience points. The trope is inverted (though it's perhaps more of an oversight) in the expansion pack Throne of Bhaal, where if you're romancing Viconia you can convince her to perform a Heel-Face Turn; doing so prevents her from using a very good item that she's already wearing—and she doesn't get a replacement to reflect the change.
Planescape: Torment is a strange case. You can get useful items or stat increases from, or confer stat increases to, almost all your party members by talking to them. The only real exception is Fall-From-Grace, who in a more conventional game would have been a potential romantic interest, but she can help you understand your party members better, cluing you in on which dialogue options to take—and also doing so earlier than the game would normally allow. Annah, meanwhile, is deeply attracted to you; you have the option to kiss her at one point, and it boosts her morale—until she gains her next level, where it returns to normal, possibly due to a bug. (For context reasons, let's now reveal that Grace is a chaste succubus and Annah is descended from fiends.)
Not a romance, but Dakkon's karach ("chaos-matter") blade becomes more powerful as he levels up. However, how it becomes more powerful depends on how he feels about you. If he finds you honorable and worthy of his service, his blade becomes an excellent defensive weapon; if he hates you, this is reflected in his blade becoming vicious and serrated; if he has no real opinion one way or the other, it's a balance of the two. This means he's probably better as a pure melee fighter when he's angry at you...but if he gets angry enough, he will attempt to kill your ass.
Not a romantic example, but there are a fair number of Pokémon who will only evolve if the trainer keeps them happy and builds a strong relationship with them.
Also, the move Return gets stronger the more the Pokémon likes the trainer. The reverse is true with the move Frustration.
A handful of NPCs will teach moves to a Pokémon only if it loves its trainer enough, or give the Pokémon a ribbon, or will give you an item if the first Pokémon in your party loves you enough.
In Knights of the Old Republic II, you can train certain characters as Jedi if you get your Influence score with them high enough. Even characters who can't become Jedi still offer other bonuses, such as experience points and stat boosts.
Ar tonelico is a series of pseudo-dating-sim-esque RPGs practically built around this trope, as you gain most of the game's musical spells by "diving" into the female characters' inner mental worlds and helping them fix their issues, an act which the game specifically links to romance. Furthermore, the characters' power in battle is increased by "Harmonics", a set of two gauges which represent the feelings of the fighting party and the magical songstresses respectively, which add status boosts to the party when the bars meet in the middle; the bars increase when the fighting party defends your singer-mage, attacks on her behalf, or does something otherwise suitably impressive for her.
Incidentally, "diving" at level 5 and beyond is when things get (supposedly) dangerous. And any and all innuendo before this is blown out of the water as their "inner" selves quite literally jump the protagonist. In a bath towel, a Y-shirt or as a succubus.
Subverted in Wizardry 8, where it's Level Down At Intimacy 5. You gain the trust of the Rapax Templar by making one of your party members an initiate. As the final task of this ceremony, the character must make a "sacrifice" to their demon queen, which basically means that the initiate (male, although she will take a female if the party is entirely composed of women) has to sleep with her. The bad part is that the lucky guy ends up permanently hexed and suffers massive stat loss if he ever leaves the Rapax Ravine until the demon queen is killed. As if that weren't enough, if you actually go through with this, it makes the already tough fight with the Rapax prince harder as—in addition to his entourage—he'll also be accompanied by the daughter of the demon queen and the character that slept with her. While this all sounds like a raw deal, being a Rapax Templar does have its advantages, and can lead to a really awesome quest down the line.
In Star Ocean (really, any of them), various bonuses you can pick up from having good relationships include (in the second one alone): special techniques, random items, improved item creation, and if in battle, doubled attack power.
Having a good rapport between your party members is essential to teamwork. For example, in The Second Story, if you choose to have your B team fight, it's likely the AI-controlled members will just do their own thing, even if they are assigned to healing duty. If Noel doesn't particularly care for Dias, he'll probably take his sweet time casting Dispel to cure Dias' paralysis.
In Mana Khemia: Alchemists of Al-Revis, Roxis won't be able to learn some of his spells unless you follow his character quest up to a point, and he won't be able to participate in Co-op Synthesis unless you follow it further. No other characters' abilities are affected by their character quests, but your Variable Strike gets stronger as your Relationship Values with the participants increase.
Also, if your relationship isn't high enough with any of your teammates (if you haven't finished their character quest and talked with them in the final chapter) you'll end up with the bad ending as the only reason Vayne doesn't go through with his original despair driven suicide is that the character you have the highest Relationship Values with snaps him out of it
While you don't actually level up from it in Dragon Age: Origins, you do gain influence - and can lose it, too, based on your actions. Sufficient influence with a member of your party grants them bonuses from the inspiration your character provides them. Negative influence, on the other hand...
Dragon Age II follows the suit by giving your Companions unique bonuses/passive powers upon reaching high levels of either Friendship or Rivalry, such as the shieldmaiden Aveline taking 10% damage for Hawke if her Friendship was maxed out.
In Raidou Kuzunoha vs. King Abaddon, your Mons will gain a new skill when their loyalty is maxed out. This is the primary method of gaining passive abilities, which are sorted differently from attacks.
And the more Loyalty you gain, the higher Raidou's Rank becomes (some ranks are just awesome: Morning Star, or Taisho Examplar), but also: at certain levels, Raidou is gifted with more tubes, allowing him to hold more demons.
In Monster Rancher 2 (not sure about the other installments), your monster's relationship values have a major game mechanic effect. Monster with low Loyalty are much more likely to fool around during fights, disobeying your commands and leaving themselves open to attacks. If a monster gets too spoiled, it will often refuse to do its training exercises, while a monster that fears you too much gets stressed out (shortening its lifespan) and is likely to run away. How you treat your monster can also affect its Good-to-Evil axis, which both affects its behavior and its access to certain techniques.
Alpha Protocol gives you "perks" for getting into bed with various women which adds a couple of in-game benefits. It also gives you experience points, so it's always funny to see Mike level up just after doing the dirty. Oh and the game has six achievements based around sex - five for having a good night and one for abstaining. You get perks whatever you do. Perk list
Earning the loyalties of your squadmates in Mass Effect 2 increases their effectiveness in the Suicide Mission and unlocks an additional power for them. Shepard also benefits, as they can choose one ally's loyalty power for their own use. However, doing the actual romances does not bring any gameplay benefits to Shepard or his/her partner.
Building a healthy rapport with Yeoman Chambers gives you the option to have her feed your fish, so they don't die if you forget to do so after every mission.
Which plays into the third game. Getting Chambers to feed your fish in 2 and then ensuring she survives the Ceberus attack on the Citadel is the only way to get one of the Intel stat bonuses.
In Septerra Core you may lead lead Grubb and Led to start a romantic relationship witch each other, which rewards both of them with unique special attack.
In Xenoblade Chronicles, raising the affinity between your party members allows them to equip each other's skills, increases the effectiveness of chain attacks in combat, and makes it easier to craft high quality gems.
In Skyrim getting married has a number of benefits.
Your spouse will open up a shop to keep themselves occupied while you're away, and you get a cut of the profits (approximately 100 gold per every 24 hours). You can also buy and sell items from your spouse as you would a regular merchant.
Once per day your spouse can prepare a homemade meal for you that increases the rate of health, magicka, and stamina regeneration.
Sleeping in the same house as your spouse gives you a temporary buff called "Lover's Comfort" that increases the rate of skill-learning by 15% for eight hours.
Harvest Moon: A Wonderful Life requires you to betroth a girl and have a baby in order to advance the story.
AWL (and AWL: Special Edition) arbitrarily has the bachelorette with the highest affection towards you propose to you, if you aren't already engaged at the cutoff point (in this scenario; usually Celia or Muffy if you haven't gone after one specifically). You get a Non Standard Game Over if you say "no". In the other games, wives raise your overall rating and unlock various items and events. (In the older games, you would get a failing evaluation without a wife)
If you don't marry in Rune Factory 2, then you can't play as your child and finish the game. Luckily, three of the prospective bachelorettes will never marry anyone but you and you have a few years to choose from all of them. However, the game does have a preferred marriage and none-too-subtly assaults you with images of First Girl Wins from the opening sequence onwards.
In Rune Factory 3, the higher your friendship/love points with a villager, the longer they'll stay with you accompanying you into dungeons (At the lowest level, they'll bail out after 5PM, then 8). Your wife will stick with you no matter how long you stay in a dungeon (VERY helpful when slogging through the last couple of Bonus Dungeons).
In newer versions of The Sims, Romance oriented Sims have as their main life goal to have as many love relationships as possible. This gives them happiness and points with which they can buy game-enhancing items. And, all jobs in the Sims require maintaining a lot of friendships to reach their higher levels.
In The Sims 3, Sims gain Charisma skill when they WooHoo with other Sims. If it is enough of a gain to move them up to the next skill point, it's more than a little funny to get the announcement while your Sims sit on their bed in post-coital bliss.
In Die Fugger II, a simulation game based on medieval European commerce, you were expected to take a spouse and sire a child. At certain points in the game, your character would die, and if you had an heir, the game would continue; otherwise, it would end.
Turn Based Strategy
In Sakura Taisen, the more one of the girls likes Ogami, the higher her stat bonuses. In addition, a high enough trust rating will unlock special attacks.
These include giant mecha that transforms from a theater.
And a hot springs bath that makes mecha explode.
Fire Emblem: Genealogy of the Holy War uses this with a twist: it's limited to romantic relationships, and in the second half you play as the characters' children. Their abilities depend on who supported with whom in the first half. The second generation characters can be paired up as well, but this only gives the usual stat bonuses since the game ends before a third generation can show up. Additionally, sometimes the partners in a relationship can give each other stat point increases or great items. Later games are similar, but that falls under Relationship Values.
Fire Emblem Awakening takes it back to this trope by again allowing for child-bearing romantic relationships, although the non-romantic supports are still present (and the main character can support with any character of either gender, with romance being available with any character of the opposite gender up until getting a husband/wife. Including the child characters (Time Travel Romance is involved), which means that most of them have different conversations for whether or not the child is the main character's child (and Morgan, who is always the main character's opposite-gendered child, has at least three different sets of conversations with some characters—one as their younger sister (or younger brother in Lucina's case), one as their son/daughter, and one as a romantic interest—and in some cases, a same-gendered, unrelated Morgan could also have an A-level conversation available)). The "Future Past" DLC really hammers it home.
Sengoku Rance, as well as the other games in the series, love this trope. As relationship goes up, characters get stronger, to put it in a simple way.
In Record Of Agarest War, you have to raise the affection level of a potential Love Interest before you can even choose her to be the mother of your child for the next generation, and the higher her affection, the more of her stats gets passed on to said child.
The warrior Iris from Princess Waltz is formed from the combination of the Prince and a Princess, with her powers determined by the level of intimacy between the pair. Being one of "those" sort of games, the Mentor notes that sex can be very helpful in making the pair comfortable with each other's bodies.
Wide Open Sandbox
Grand Theft Auto: San Andreas has this. Six girls you can date, in exchange for perks, like weapons, clothes, their cars, the possibility for dying/getting busted without losing all weapons, and, in one of the girls' case, a plot advancing MacGuffin for a mission.
Non-video game examples:
Anime and Manga
In Lucky Star, Konata says that to her, building up "trust points" in the days before Valentine's Day is more important than the day proper.
The World God Only Knows is an interesting case. Runaway spirits are beings from Hell that feed on negative emotions. Therefore, the best way to chase them out is to use positive emotions—specifically, love. However, beings from Heaven are the opposite, and are directly strengthened by love. In both cases, it is noted that a kiss is generally an important milestone. It's enough to force out a runaway spirit, and enough to give a goddess wings. At the same time, it is noted that this is only an approximation. Several times, Keima has been in situations where a kiss wasn't enough, simply because he played the card too early or there were other complications.
Persona 4 - the animation, following the video game source.
Anita Blake books are a literature example. In Anitaverse, a triumvirate of a vampire, a lycanthrope, and a necromancer gathers a big power boost over the sum of their individual powers. The catch is, to gain the boost, all three have to be very fond of each other. A triumvirate doesn't have to be menage a trois (although, it implied, it often is), theoretically the triumvirs could just be very close friends.
Literary example in Tanith Lee's novel Lycanthia. The feudal lord of a certain lineage, when having two werewolf companions, gains the magic powers of an ancient wolf goddess - but only if all three are in a state of true love (not necessarily sexual). The powers are implied to be immense. The protagonist doesn't feel true love to his werewolves, just a kind of needy affection - but even that is enough to summon a hailstorm at a critical moment.
Near the end of Illuminatus!, this has to be used repeatedly by one character to become an avatar of a goddess.
HeroQuest (the fantasy tabletop rpg set in Glorantha, not the MB boardgame) stats everything up, including relationships. Also, any stat can be used to augment any roll provided you can make a case for it to the GM, so your "love for kidnapped princess" score gives you a bonus to fight the dragon, and your "hatred of nuns" score makes it easier for you to kick one in the face.
Weapons Of The Gods has you improve your kung fu by consummating your love. However, it only works in heterosexual interactions - for homosexual interactions, you need a special kind of kung fu to improve your kung fu. It doesn't sound this offensive once you read the book, and it's based on Taoism. Heterosexual intercourse allows for the unity of yin and yang, male and female, which is a major theme in Taoism.
Legends Of The Wulin, Spiritual Successor and sequel to Weapons Of The Gods, likewise has mechanics for strengthening your partner's chi through sex. As above, it normally only works with heterosexual actions; homosexual male sex is damaging to both partners, female-female sex is simply not sex for kung-fu-related purposes. This can be gotten around by developing the proper Daoist Sexual Technique.
Monsters And Other Childish Things places a heavy emphasis on relationships. Kids can draw upon their relationships to give them an extra boost when needed, like punching someone who insulted their brother extra hard, or doing better on a test if their mother encourages them. Monsters can also draw upon a child's relationship for an extra boost in combat, but if a relationship boosted roll fails...
Any Tabletop RPG in which the DM is in the habit of giving players extra XP for roleplaying can have examples of this.
Maid RPG has seduction built into the rules, and both sides benefit: The seducer loses Stress, and the seducee gains Favor.
Pv P plays on this trope in this comic, where Francis and Marcy level up upon losing their virginity to one another. Their physical appearances noticeably change, making it harder to hide the fact that something happened.
The web serial Memetic Narration (found here) features high school students who get sucked into a computer and fight turn-based rpg battles. Their available abilities are affected by their relationships with each other, so the main character (being the only one who knows of this) works hard to befriend each of his teammates.
In Real Life, marriage (but not anything else) unlocks lots of special rights and financial bonuses that make it easier to get a high score and a better game experience. It also makes pregnancy and being over certain age much more acceptable. Won't prevent death but makes you less pitiful during it.
To put it another way: marriage doesn't require Intimacy to be at level 5 in order to initiate, but having it at a high level makes divorce less likely, and regardless of what the players' intimacy levels were at the beginning, it may or may not end withlosing half of your items and a lot of prestige (again, depending on server and current rules in effect).
Another Real Life example, studies show that being regularly sexually active (no marriage required) has numerous minor health benefits.