The Fallout series is set in a post-apocalyptic Scavenger World in which getting an old car to run is a major quest. However, it's a world that's on its way to fill the holes: in the good endings of both Fallout and Fallout 2 new cities are created, new governments established and it's implied that things are going better. It should be noted that the scarcity that seems to have hit the automotive industry has apparently left the weaponry one untouched, at least judging by the ludicrous amounts of energy blasters, miniguns and assault rifles scattered all over the place. They did manage a Hand Wave with one character late in the game, a blacksmith who produces his own gunpowder and loads it into recycled shells to make new bullets for sale.
Fallout 3 takes place on the opposite coast of America, and is much closer to this trope. Megaton for instance is a town with houses, furniture and outer walls made out of scrap metal from an old airport. It also affects gameplay too, as buildings that you've picked through for supplies stay empty. The armor used by Raiders and Super Mutants are made from scavenged materials, such as car parts and old tires. One piece of concept art for the Super Mutant Behemoth depicted it wielding a car engine attached to a chain as a makeshift flail.
Fallout: New Vegas is less of a scavenger world, given how there are factories building new weapons and ammo, as well as gear. Much more new material is also produced and created than before- though scavenging is still a good way of finding weapons and cheap items to sell.
Which is consistent with in-universe explanations of just how the world worked after the bombs fell. The knowledge wasn't lost—-it was just sealed away on old Vault computers and in military bases like the one the Brotherhood of Steel got its start in. Which is unsurprising when you consider that New Vegas was helmed by a lot of the same people who did the first two Fallout games and is much more consistent thematically with them than is Fallout 3.
In one quest, you're asked to shut down one such factory. Why? It's making bottle caps, the universally accepted currency in the Wasteland, and making more would crash the market.
In the spirit of post-apocalyptic worlds like Fallout, old CRPGs like "Visions Of Aftermath The Boomtown" and "Scavengers of the Mutant World" are good examples of old survival/scavenging games from the old PC era
NEO Scavenger: A Post-Apocalyptic Survival RPG is a game basically going around surviving and resolving the main story via scavenging
BattleTanx: Nominally what the world is supposed to be. Yet somehow EVERYONE seems to be effective enough scavengers to all have tanks...
The Blastia in Tales of Vesperia. It's stated that there is no known way to create the Barrier Blastia used to keep monsters away from cities, along with most other Blastia. This is because excessive blastia use in the past created a planet-eating Eldritch Abomination, so the knowledge was destroyed and the surviving blastia were all given to one family so that they could be regulated.
This happened in EVE Online's backstory: When the wormhole connecting the New Eden and Earth collapsed, most of the colonies died off or regressed back to pre-industrial status due to the lack of self-sufficient infrastructure. It got better, but there's still plenty of Lost Technology to be found.
This trope is invoked constantly in Xenogears. Lesser technology, including Gears, is scavenged by previous civilizations that died out. More advanced technology is scavenged from the ship and cargo that originally crash-landed and brought humanity to this planet 10,000 years prior, as seen in the intro movie. In fact, all of the technology that had ever been used in the game comes from the Eldridge; the Galactic Federation that produced it was pretty high up on the Kardashev Scale.
Played with in Borderlands: people on Pandora tend to scavenge and salvage gear and tech, but it's implied that it's because Pandora never really had an industrial base to begin with, and most of the people on planet were convicts. Also, it's implied that this situation is fairly unique to Pandora; it's mentioned at least once that Pandora got supply drops from off-world.
The main protagonist of Septerra Core grew up on a world shell where the most common way to make a living was by scavenging scraps dropped from the higher, more affluent world shells.
Mass Effect: The Krogan homeworld of Tuchanka is this — essentially a planet-sized postapocalyptic junkheap whose inhabitants no longer care about making things but instead concern themselves with fighting over the few remaining scraps of technology. And the Krogan like it this way, because it apparently proves how tough they are.
Phantasy Star Zero has a LOT of this. The world's gone to pot, and pretty much everything remotely advanced has been scavenged from the ruins. Scavenging ruins for relics (whether usable or reverse-engineerable) is a full-time profession, often as a civil service. In fact, one of the major storyline quests involves scavenging a suitable CAST body for an ally from a ruined city.
Phantom Dust has technology that looks like it was jumbled together from all sorts of tech. They seem to be set for equipment, though, so the few scavanging missions you go on usually has food, recipes, or medication as the goal.
In Chrono Trigger, there is a sidequest early on which involves locating food for a group of survivors in the Bad Future. Unfortunately, by the time you do find it, it's all spoiled because no one was left to run the refrigeration (or it simply didn't work). Also, it's worth noting that the reason you're doing this is because the survivors have been heretofore relying upon a machine that replenished their health instantly, but as the party notes, it could break down at any time, and no one knows anything about fixing it.
Breath of Fire III has intensive use of machines built from scrap parts from an unknown origin and people don't have the knowledge to reproduce them.
Likewise does Megaman Legends from the same publisher, which has a scavenger world that looks and feels quite similar to BoF3. Legends 1 even thanks the "BoF3 Rescue Team" in its credits.
The settings of Planetarian. The viewpoint character's job is raiding depopulated ruins of cities to find MREs, or just anything that is potentially valuable. It's not an easy job because the competition is cutthroat, and the ruins are patrolled by autonomous death-machines that are supposed to defend the cities, even if they are pointless because the cities are no longer inhabited After the End.
I Am Alive is the most scavenger-y of them all. How many bullets do you usually find at a time? ONE.
The Facebook game Wasteland Empires is all over this like white on rice, at least for the first four tiers, after that it appears you start a steep learning curve with recovering the old technology.
The Lost Colony◊ in X Rebirth has an old Split Python (a destroyer from the X3 trilogy) stripped for supplies, with power lines leading from the ship to a nearby installation. The shutdown of the jumpgate network at the end of the Terran Conflict set off a dark age for many small colony worlds; De Vries, a cut-off Terran colony, suffered greatly at the end of the Terran Conflict, as it wasn't self-sufficient - tens of thousands starved, and many went insane and started looting other stations. When it's reconnected to the shattered remains of the gate network thirty years later, most of its ships are cobbled together from old United Space Command hulls, and the majority of the population live in the wrecked hulks of old Terran mining stations.
Metro 2033 is a Post ApocalypticCrapsack World taking place in the subway tunnels of Moscow After the End, when a nuclear strike irradiates the surface almost beyond survivability and plunges everything into a nuclear winter. The few creatures and people who survived above-ground have become horrific mutants of some form or fashion. Most of the equipment found or seen is put together from bits and pieces of pre-war technology or repurposed altogether. This is most evident in the weaponry. While guns are obviously a necessity in the game's setting, all the better to hold off bandits or the occasional monstrosity that approaches a population center, the weapons that are there are generally cobbled together from pipes, plywood, and parts of proper guns. The game's basic double barreled shotgun and SMG equivalents are the guns that are most obviously built from scavenged pieces, as they are visibly and obviously constructed from pieces of old plumbing with receivers and stocks welded on. The sequel adds even more scavenged weapons, like a bolt-action rifle that's visibly built up from parts of two different guns and a flare gun modified to fire shotgun shells.
The housing situation in both games is no better, with the denizens of most stations living in either shabby huts made out of plywood and sheet metal or ersatz "apartments" built from empty subway cars.
The "Developer Pack" DLC in Metro: Last Light actually features a multi-barelled shotgun built with nothing but scavenged bicycle parts.
Played with in Warzone 2100; salvaging pre-Collapse military technology is a key game mechanic and indirectly kicks off the plot, but when you find it, you have your engineers reverse-engineer it and put it back into production.
The iOS game Rebuild involves survivors of a Zombie Apocalypse trying to rebuild human civilization while fending off attacks by zombies and raiders, finding more survivors and convincing them to join you, reclaiming zombie-infested areas, sending people out to find food and supplies (which you can't build yourself), etc. You can even reclaim labs and research new techniques in them, including the zombie virus cure (one of the ways to win). Some equipment can also be purchased from or sold to a visiting merchant for food. The equipment includes weapons (anything from a chainsaw to an assault rifle), dogs (which the game treats as equipable weapons), tools (and yes, some tools, like sledgehammers, double as weapons), leadership items (e.g. a megaphone to talk to survivors or a Nice Hat) and scientific equipment. Each survivor has stats associated with various skills (killing, scavenging, leadership, research, construction), which improve with successful use or equipment. The game never has you run out of ammo, though.
Red Dead Redemption: Undead Nightmare applies this to the original game's setting. Nobody's selling any goods now. You've got a horse on call, but that's it. If you're lucky, you'll get back enough bullets after a fight to replace what you spent on the fight. Bait? Bombs? Any other tools? Make them yourself.
Another prime example is the setting of Rapture in the BioShock series, where security bots are mad from boat parts, turrets are chairs with guns duct taped on with motors to move them, and the grenade Launcher fires canned goods as explosives and it's loaded to a box filled with said canned goods.