Mario (and possibly Luigi) with Peach in the Super Mario Bros. games. Of course, the very nature of their relationship itself is very vague because of Nintendo's policies and Peach usually just rewards Mario with a kiss on the cheek. Surprisingly this issue is pretty much directly addressed in Super Paper Mario when Luvbi asks the characters if Mario and Peach are an item. If the player has Mario out he shakes his head in denial, or if Luigi is out instead he will say that it is "kinda hard to say" but that he wouldn't call her Mario's girlfriend. Luvbi concludes it as a one-sided crush.
Link and Zelda (as well as Marin, Midna and any number of his female companions throughout the years) in The Legend of Zelda series.
It seems that all Zelda games in the Adult Timeline (The Wind Waker, Phantom Hourglass, the latter half of Ocarina of Time and Spirit Tracks), all have a love interest between Link and Zelda, most notably Spirit Tracks, wherein it is clued several times: When Link and Zelda first meet, Link blushes, then at the end of the game immediately after Zelda reclaims her body, she gives Link a hug, causing Link to blush, which seems innocent enough, until after the final boss, Link and Zelda hold hands, which is much less innocent than it sounds. UST is restored at the game's conclusion, though, as Link returns to his engineering, becomes a warrior trainee, or just departs from Zelda's life depending on the choice the player makes near the end.
The end of Skyward Sword heavily implies that (at least for those incarnations of Link and Zelda) the tension will most likely be resolved soon enough, given that they stay on the surface together to found what would become Hyrule.
The player and either Carth or Bastila (depending on gender) for most of the first Knights of the Old Republic, and the player with Atton or the Handmaiden in the sequel.
Ada Wong and Leon S. Kennedy from Resident Evil. Some could also be argued for Billy Coen and Rebecca Chambers, but with Ada and Leon, it's definitely harder arguing against it. Ada's thoughts and actions are a pretty clear indication that Ada genuinely loves Leon, but can't seem to act on it due to circumstances. Ada is pretty much "Catwoman" to Leon's "Batman".
Chris Redfield and Jill Valentine also seem to have plenty of this going on as well. Ever since REmake, the series has been filled with not so subtle signs of a deeper affection whenever the two are onscreen, even though it's never been taken further. Even Chris's new (working) partner Sheva in Resident Evil 5 makes the quick deduction that he and Jill were "close" after he recounts a brief description about her.
In regards to Billy and Rebecca, it's interesting to note that neither have had any canonical appearances since Zero/REmake, though both are still alive.
Fox and Fara shared that experience as well - but at least they never split up.
In the Metal Gear series, Solid Snake and Otacon are suspected of this. Even creator Hideo Kojima is a fan of the unstated pairing. This was essentially confirmed in interviews with the voice cast, where David Hayter has admitted that he and Christopher Randolph played Snake and Otacon as a gay couple.
Mass Effect 2 has this develop between Shepard and Samara if a relationship with her is pursued. Considering Samara is a Celibate Hero, it remains in the "Unresolved" stage... unless you get "The Citadel" DLC for Mass Effect 3.
Conversations between Shepard and Liara, and (male) Shepard and Miranda have shades of this in Mass Effect 3, if they were left unromanced through the course of the trilogy.
An accidental version was the sexual tension between male Shepard and Kaidan in the first two games, largely caused by a combination of the option to resolve it being removed from the final versionnote In the first game and setting very little different dialogue aside for romanced FemShepsnote Especially in the second game. Large numbers of fans noticed and the combination became very popular for a then hypothetical Gay Option. Bioware took notice of how popular the pairing was and made it a legitimate option in the third game.
Persona 3 is chock full of this, especially when it comes to a (Male) Protagonist and Yukari. The game blatantly puts the two together in would-be romantic situations outside of her Social Link, but when you max out her Social Link, she admits her love and tells him not to make plans that evening...and ends with a rather ambiguous sentence about what came after (something that carries over into Persona 4). And given the ending, the amount of UST could be irksome.
It even carries into Persona 3 FES's Playable Epilogue, The Answer... the protagonist's death clearly affected Yukari very deeply.
People believe Lara Croft and Larson in Tomb Raider Anniversary behave this way. Larson doesn't try to kill Lara over the first Scion piece until he is losing the fight and Lara never makes an attempt to shoot Larson at all, but uses fancy acrobatics to knock him down. In another scene, Lara attempts to escape from Natla's goons and Larson had a clear shot at Lara, but purposely misses his shot. In the two characters' final meeting, Larson gloats that Lara doesn't have what it takes to kill him and he just stands there believing it until Lara actually starts shooting him in a Quick Time Event. Should you fail the QTE here, Lara gets killed and Larson regrets that he had to kill her.
In Dragon Age II, if Hawke slept with Isabela but later romanced someone else, subsequent conversations indicate that despite her claims that it was simply a fling, Isabela actually cares for Hawke far more than she lets on.
In the Phoenix Wright: Ace Attorney series this might just be going between Phoenix Wright and Maya Fey, although this is purely hypothetical. Maya's younger cousin Pearl Fey is absolutely sure this is just what's happening and Maya acting rather annoyed (and possibly jealous) at Phoenix knowing Adrian Andrews, while Maya herself has never met Adrian, when they meet her in the third game might be a hint. Yet again, this is very hypothetical, but there are some interesting hints if you know where to look. There are also a few hints at an unresolved sexual tension existing between Phoenix Wright and Miles Edgeworth, which is supported by a few possible hints as well but is also highly hypothetical.
Saints Row 2: The British Male voice-set for the Boss seems to believe there's some of this going on between Pierce and Shaundi, sometimes randomly remarking "I wish Pierce would quit bitchin' about Shaundi and just fuck 'er already."