Used in Dungeons & Dragons, where demons and devils can be summoned to make pacts with mortals, and can grab your soul and run if you mess up the pentagram or leave out the "Promise not to kill me when you're done" clause in the contract.
Fiendish Codex II: Tyrants of the Nine Hells has a whole section detailing Faustian pacts. Devils prefer to strike a Pact Certain with a foolish mortal willing to explicitly sell their soul to an archfiend, but more commonly use the Pact Insidious. This approach doesn't directly damn the mortal to Hell, but they must trade a service for the devil's offer of assistance, treasure or magical powers. Many mortals believe that they can reap the rewards of such devilish pacts without suffering the consequences, unaware that each corrupt act they perform in exchange is another step towards damnation. The devils, meanwhile, usually make arrangements for their "partner" to die as soon as their soul is marked for Hell, to avoid any chances of atonement or deathbed repentance. There are only two grounds for exemption in these pacts: if the mortal was coerced into them, or if the devil didn't deliver the goods as promised. A sufficiently knowledgeable character can in fact protest along these lines and take their case to an infernal court, and since devils are as Lawful as they are Evil, they will offer the plaintiff a fair trial, even providing legal counsel as needed. A combination of Knowledge (the planes), Diplomacy and Perform (acting) checks can see a mortal's soul freed from a devilish contract... but even if the mortal wins their case on merit, it's possible that their other actions have damned them to the Nine Hells anyway. "Much diabolical laughter then ensues."
Demons are generally too Chaotic Evil to make such complicated, long-term plans, but the demon lord Pazuzu is known to take an active interest in mortal affairs. Anyone who says his name three times grabs his attention, and after telepathically scanning them, the Prince of the Lower Aerial Kingdoms will teleport to them and offer his aid. Any who accept it will shift their alignment one step closer to his, yet the notion of a demon lord for an ally is rather tempting, especially since Pazuzu is canny enough to take care that no evil emerges from his assistance (at least the first time).
The Warlock is a spellcasting class that gets its powers from pacts with extradimensional entities. That said, they don't have to be evil, and the creatures they deal with don't have to be devils - warlock pacts can be made with demons, fey, creatures from the Far Realm, subterranean horrors, sorcerer-kings, and so forth. Such powers are generally evil or at least alien, but again the warlock is not automatically evil for making these pacts, and can actively work against their patrons with their own powers. The 3.5 version also mentioned that the deal doesn't necessarily have to be made by the warlock themselves — some deals could be inherited and remain dormant for a few generations until some poor fellow gets saddled with powers from a deal he never knew about. The 5E version, in addition to having outright and archetypal Good patrons, also emphasises that it is possible to con the patron and end up with a pact that obligates them to provide power in exchange for the warlock keeping their soul and being free to do what they want.
Binders are accused of this, and practice what is called Pact Magic, but it's not a traditional deal with the devil. The Vestiges they call up are fragments of sentience beyond normal conceptions of life or death, and the bargaining process only determines whether they will be able to influence the Binder's behavior in quirky ways before granting their Powers via Possession.
The sourcebook Evil, true to its style, contains some rules for how to handle deals with devils and demons, including a list of benefits (and their downsides) that you can get, typically in the lines of "get superpowers but look and/or smell demonic."
Van Richten's Guide to Fiends for the Ravenloft setting contains part of the actual text of such a deal, between a human man and a succubus (for sexual favours, of course). It sounds a bit like a typical software license agreement a computer user would agree to without reading, though in this case the man accidentally doomed his wife to be murdered by accepting the part involving the removal to any obstacles to the deal, including the elimination of "any organic organismsnative to the environment in question."
The Gates Of Hell describe the details of such deals for most of the Hell nobility featured. The book also includes the catches. For example, one devil can give bonuses to fighting skills. However, as you get them, you get penalties in other areas. At the end, you must fight an Evil Twin of yourself, the twin having the bonuses, but you only having the penalties. If you somehow manage to win, you get more bonuses, but then have to repeat the same fight, except the Evil Twin has more bonuses, and you have more penalties. Eventually, you have to fight the devil himself. No one knows what happens if you defeat him, since that never happened.
Pathfinder has plenty of examples, and there's a specific type of devil, the Contract Devil, that specializes in this. In addition, there are several notable examples in the setting itself.
The Thrice-Damned House of Thrune, the ruling family of Cheliax, gained power through a direct deal with Asmodeus during the country's civil war. Despite this, House Thrune does not worship Asmodeus, and often clashes with his faith.
In Curse of the Crimson Throne, Ileosa makes a deal with a belier devil and his master, the exiled Duke Lorthact, binding an Eyrinies to herself in exchange for her soul (though Ileosa was already evil, as a Neutral EvilNay-Theist, she would have gone to Abbaddon, not Hell.) and rulership over Korvosa once she is done with it.
A variation occurs in Mage: The Awakening, with the beings known as the acamoth. The acamoth make deals with mages (and possibly other mortals) whereby they consent to allow the acamoth to enter their souls and Mind Rape them. If the mage survives with their sanity reasonably intact, the acamoth are obliged to grant them powers. The acamoth are noted to not have much interest in souls which are already corrupt, and are generally concerned with inscrutable, long-term goals (ie, conquering reality), which means they will rarely take a soul outright (a comparison is made to financial investment).
Also toyed with in Changeling: The Lost. A Changeling or True Fae can bind a human to a Pledge, offering money, power, or other benefits in exchange for various favors - but most Changelings, due to the importance of contracts and pledges among the fae, are geniuses at twisting the meanings behind the words of their pledges. Not only that, but an agreement with the True Fae has a better-than-average chance of ending in the human kidnapped and subjected to Mind Rape in the True Fae's Arcadian realm. Best case scenario: he escapes as a Changeling. Worst case? You don't want to know.
Hunter: The Vigil and World of Darkness: Inferno also include rules for making dark contracts with demons; some of these are the traditional "sell your soul" variety, while others simply require you to perform actions that feed the demon's Vice. Many of these demons are actually remarkably straightforward in their dealings, and hunters often find themselves searching for loopholes and hidden clauses that aren't really there.
Mage has lots of other examples, including the Lethean (offers to take away painful memories or things you'd rather not perceive, the cost is that you're giving up parts of your memories and perceptions), the Oath of Ruin (offered one guy Awakening in exchange for coming through once he had enough living descendants, and is outright stated to only be banishable by doing something truly evil), and the Scelesti (mages who twisted their souls in exchange for power).
It shouldn't be a surprise that Demon: The Descent has these, and a nasty variant. Demons effectively make soul pacts with mortals, offering things in returns for aspects of the mortal's existence. These aspects are then used by demons to cement the Covers that keep them hidden from the agents of the God-Machine. A number of demons go for a kind of pact that's only cashed in if the demon's Cover is destroyed entirely... but if that happens, the demon can just adopt his thrall's existence instead. And the thrall vanishes. Utterly.
The most traditional variation is seen in Demon: The Fallen, in which a Fallen character can make a mortal human their "Thrall". In exchange for the usual stuff like health, luck, romance, etc., the human becomes permanently bound to the Demon and has to fulfill their part of the deal in addition to supplying their master with Faith (used to cast magic). Thralls do have free will and can contemplate a Faustian Rebellion but the only way to break the connection is actually killing their master, which is not exactly simple. Additionally, there are the Earthbound, who Mind Rape their Thralls to make them completely obedient slaves (who cannot provide them with Faith, though).
The Vampire: The Masquerade supplement Guide to the Sabbat had rules for Dark Thaumaturgy, which is Thaumaturgy taught by demons, frequently involving a Faustian pact. Aside from the hatred and fear with which many infernalists (as Dark Thaumaturges were called) were viewed (especially the Sabbat, who are very big on not being under another being's thrall), the rules even specifically stated that the Storyteller now could have the character dragged straight to Hell at any given time, like, say, if they felt the character became TOO powerful.
The Chaos Gods of Warhammer and Warhammer 40,000 often empower their mortal followers: Khorne can bestow martial prowess and brute strength, Tzeentch can grant a worshipper sorcerous power or fate-weaving cunning, Slaanesh boosts a person's charisma and makes their senses keener, and Nurgle's followers have their lifespans increased and become significantly tougher. In rare cases, these pacts work out. More commonly, Chaos worshippers fall prey to the very pacts they made: Khorne's followers become mindless killers consumed by bloodlust, spilling their own if no foes present themselves. Tzeentch's devotees end up power-hungry, paranoid, and trapped by the complexities of their scheming, or even betrayed by their patron as part of the god's Gambit Roulette. Slaanesh's disciples become addicted to sensation of any kind, be it mind-rotting drugs or self-mutilation. And Nurgle's cultists are turned into festering, putrid husks, whose corrupt bodies are so tough because they're rotted past the point of feeling pain anymore.
In any case, the road of a champion of Chaos only has two destinations: ascension to a full-fledged daemon prince, or else all the gifts and mutations cause the aspirant's mind and body to collapse into a bestial chaos spawn.
The best part is since these are gods of chaos, making a pact with them in the first place can be difficult - they're just as likely to notice and reward some dabbling nobleman than a warrior who battled for decades in their name.
You can make these pacts in the Dark Heresy RPG, though it may be hard to keep them concealed from your teammates...
A really bad Faust comes from the Warhammer spin-off Mordheim. Nicodemus asked a Greater Daemon of Tzeentch to become "the greatest wizard of the Old World." Wish granted. He discovered an antidote before he grew too large, but he requires a constant supply of Warpstone to manufacture it.
Mutants And Master Minds has one in the form of Mr. Infamy, who looking to make this kind of deal. It doesn't matter if it's a normal Joe, a superhero or a supervillain.
Exalted has a number of versions, seeing as tacitly summoning and bartering with demons isn't exactly frowned on by the religion of the Realm, but the most traditional might be Abyssal Exaltation. One of the Deathlords comes to you on your deathbed and promises you a second chance at life, as well as power beyond your imagining... as long as you'll bind yourself to his service, throw your name into the Void, and aid him in the destruction of Creation.
And then there are the more traditional devils, the Yozis. One of the ways the Yozis recruit the Green Sun Princes is to go to a mortal who had a chance of performing great deeds that would have lined them up for Exaltation, but backed down in the face of adversity. The Yozis then offer them a second chance at greatness...
And then there are the akuma, Exalts and "enlightened" mortals who threw their lot in with the Yozis. The resultant procedure gives them great power, rapes their free will out of existence, and turns them into a very intelligent oven mitt with a daiklave. Yeah, becoming akuma is rarely a good idea.
Among the Green Sun Princes, the favored of Cecelyne can make these and dictate terms thanks to the Verdant Emptiness Endowment Charm, which allows them to answer wishes made even in jest. Further Charms allow them to grant further benedictions and heal the grievously wounded... as well as revoke their blessings, painfully, if payment isn't offered up.
The fan-made "Terrifying Argent Witch" remake of the Lunars enables them to play the part of the Devil; fulfilling a spoken desire (serious or not) in order to "buy" someone's shape (and possibly soul, given how Lunar shapeshifting works), sealing oaths in blood (complete with a terrible curse should they break the pact), lending power at the cost of being emotionally tied to the Witch in question.
This is a large part of Black Magic in Magic: The Gathering. The most up-front about it are the demons you can summon and involve a "payment", a drawback in the form of having to sacrifice other creatures, discarding cards or losing life. Note the flavour text on the latest reprint of the classic Lord of the Pit: "My summoning begins your debt, planeswalker". The character Liliana Vess has a major deal with dark forces in her backstory.
A lot of cards involve making some payment (usually life) to some dark force to gain some benefit (usually cards), for example Sign in Blood, Vampiric Tutor, Death Pit Offering, Tainted Pact, Yawgmoth's Bargain, etc., but the game's most egregious example however, remains Contract From Below. A long out-of-print card that used the infamous "ante" mechanic of the game's early days. It allowed you to draw a fresh hand of 7 new cards, but required you to bet a card from the top of your library on the outcome of the game. There is a reason that Contract, and other cards with the "Ante" keyword, have never seen reprint.
Abyssal Persecutor is a 6/6 demon with flying and trample that costs only 4 mana. The catch? You cannot win the game and your opponents cannot lose as long as he's in play. However, he can still be quite useful if you have a way to get rid of him after using him to down your opponents' creatures and life totals.
A more recent example would be the aptly named Demonic Pact, which after played, gives you a different positive effect for the next three turns, after which, on the fourth, you automatically lose the game.
Quite common in Deadlands. Nearly all magic comes from the spirits of The Hunting Grounds. The nice ones are in the minority. The most common playable version of this is The Huckster, who has to allow a demon into his body in order to cast a spell. Just hope the Huckster isn't tricked into giving the demon too much control.
Played straight and toyed with in Nobilis. The Cammorae play both sides. They're Faust when they make a deal for whatever powers they receive and lose their humanity. They fit in the Mephistopholes role when the player characters contract them to do something. First and second edition Powers of Hell also play with this trope. Many love buying souls, with the full knowledge that such deals don't actually do anything. Humans that think they have no soul have no reason to act virtuously, and will probably become corrupt and hellbound in the process.
In the Yu-Gi-Oh! game there is a Spell Card called "A Deal With Dark Ruler" where the card art suggests this, showing a man making a deal with Dark Ruler Ha Des, a powerful Fiend-Type Monster in the game. (The card's actual effect has nothing to do with Dark Ruler Ha Des or Fiends; it lets you summon a powerful Nomi monster called Berserk Dragon if one of your a Level 8 or higher monsters is sent to the Graveyard during the turn it is activated.)
In The Dark Eye there are twelve Demon Lords as well as several powerful so called free demons one could forge a pact with to gain gain access to special powers depending on the lord and being able to summon his or her servants more easily. The downside, aside from eventually going to the hells, is that over time anyone with a pact will start developing character traits that fit those of his demonic liege. So a person with a pact with the Lord of Strife and Movement will develop a Chronic Backstabbing Disorder and soon won't be able to stand still or even sleep anymore, while someone with a pact with the Lord of Slaughter and Bloodshed will become more vicious in battle and start developing wounds that always bleed but do not weaken him.
Binding a demon in Sorcerer generally involves the sorcerer offering to take care of its Need in return for it granting them its powers. Every player character starts out having already Bound one demon, potentially Binding more as the story develops.
The Shackled Court of Uncreated Night in Godbound have a particularly clever spin. Unlike most versions, which just shaft everyone who takes the offer, they periodically allow a mortal petitioner to get everything she wants without nasty little tricks or hidden costs. That way, when the petitioner runs off into the world boasting about how they managed to trick the Shackled, more people are willing to give it a shot themselves...
One sample monster in Monster of the Week, Uhul, likes to pull this, granting magical power in exchange for souls or other valuable resources.