You're a brand new adventurer, setting out for fame and fortune, and probably about to get caught up in an epic plot to unmake reality as we known it, which only you can foil.
But first, can you clear out the rats in my basement?
A common early quest in many RPGs, particularly of the Western, tabletop-derived variety. Rats may be of unusual size, or substituted with some similarly non-threatening and easily killed critter, and indeed the basement may well be a different room entirely. This may even be part of the game's combat tutorial. Whatever the specifics, there's an area filled with small squishy things that need squishing. Get to it.
Often considered a classic hallmark of the genre, and is likely to be included simply as a nod to tradition. Or, as is becoming more and more common, parodied with an unusual variety of rats.
Subtrope of Mass Monster Slaughter Sidequest. Not to be confused with Goomba Stomp.
If you're still getting these sorts of quests when you're famous and powerful, it's time to start yelling "Dude, Where's My Respect?"
Played straight in Facebook game Mousehunt. Though everything you fight is a mouse, the three weakest mice (White, Brown and Grey) the player encounters in the tutorial are based off regular varieties of real-life mice/rats while everything else is a Ninja Pirate Zombie Robot
The Elder Scrolls IV Oblivion plays it straight by starting you off in a dungeon/secret passage largely populated by rats, but subverts it with the first Fighter's Guild quest — you're told a local woman has a "rat problem" in her basement, but the problem is that they're her pets and mountain lions are killing them.
When asked about "Rumors," some NPCs will point out how the tasks given to new recruits always seem to have something to do with rats.
The Elder Scrolls V Skyrim also has an archetypal "clearing out rats" quest, but it's not possible to do it before a number of other quests have been finished. Also, exterminating pests will only be a cover for the real task...
In Hex Coda, a module by Stefan Gagne, you're asked to get rid of the rats in the basement of a bar. Except that these are mutant, anthropomorphic rats, and the best course of action is not violence, but diplomacy — you can simply ask them to leave nicely. The Journal entry for this quest is called "Ratstomp", making this the Trope Namer.
The reboot of The Bard's Tale starts with the Bard trying to impress a Barmaid by taking care of her rat problem. Turns out that the 'problem' is a giant, fire-breathing rat, and the locals regularly get a kick out of watching cocky adventurer types being beaten by it.
While World of Warcraft indeed has some quests dealing with rats, they are never a challenge - even first level quests deal with wolves, panthers, bears, giant owl-bear hybrids or humanoid bandits. The only ones that come close are a couple concerning giant undead bats A more standard example of this trope would be the Kobolds, who are a race of mining rat-people that populate the early Human player maps.
Mardek RPG: The rats have strange pipes instead of tails.
In Chinese Paladin 2, one of the earlier mainline quests involve getting rid of a rat infestation. You pick up your first summon there, a giant rat-spirit who has earth-element attacks and can also steal stuff.
The first thing you are required to do in Final Fantasy XII is to clear out the rats in a sewer. One of the local old guys even calls Vaan "Vaan Ratsbane" jokingly.
One of the weakest enemies and most common first encounters in Dungeon Crawl is the common brown rat.
The old Tutorial Island in RuneScape included a Battle 101 section, where you killed - you guessed it - giant brown rats. The rats in the "real world" are much smaller.
Planescape: Torment has a quest that gives you a bounty on rat tails. In keeping with Sigil's utter bizzarness, it is on Cranium rats, who become increasingly deadly sorcerers when in the presence of more of their kind.
Tales Of Symphonia had a subversion; you don't fight rats until around halfway through the game.
Dragon Age: Origins has the human noble fight off an invasion of rats in their family's pantry in their origin story. Like all classic RPG tropes in the game, it's lampshaded.
Oddly enough, it's the only time in the entire franchise thus far that giant rats are an enemy.
In the original Alone In The Dark 1992 you must dodge rats in a wine cellar while looking for ammunition in that room. The rats can't be killed, but if they touch you, they wear down your life force and you are liable to die.
In Arcanum: Of Steamworks & Magick Obscura, a Tarantian businessman asks you to clear the rats out of his warehouse, although this actually occurs in the second town you visit. There are a couple of opportunities earlier in the game to kill rats in dark rooms, though.
Your first task in Fallout is to head over to Vault 15 and see if they've got a spare water chip. As it happens, Vault 15 is now a bomb shelter full of mutant rats, and of course you start in the area outside Vault 13, also full of rats.
Fallout 2's Trapper Town has a serious rat problem.
And then, in Fallout 3, one of the first quests you can obtain involves testing out a rat repellent. It involves hitting rats with a stick. That makes their heads explode.
Drakensang features a brewery full of rats. This is, however, not a low-level quest.
Hilariously lampshaded later when the main characters ask to a Inn Keeper if he can obtain his trust by killing the rats in his cellar, making him angry at you. Then is double subverted when you find out that he does have giant rats in his cellar.
Sacred 2 asks you to clear out a couple of cellars toward the beginning of the game. One of them is, predictably, full of rats.
Your first quests in Noobshire from Adventure Quest Worlds has you saving rats rather than killing them, though one of the quests for Yulgar does involve cleaning out his rat-infested basement.
Any RPG made by Spiderweb Software has a good chance of having rats as the very first enemies you fight, before you even go on any quests.
One of the first things you do in Brain Lord is help clear one villager's attic of rats.
For the first part of any Pokemon game, one of your major annoyances will be the Rattatta coming at you every time you hit a patch of grass. Except for Gen V, where it's Patrats.
EVE Online, even being a Wide-Open Sandbox, is not immune, except the rats are low level NPC pirates in spaceships...which the players call "rats", and the act of cruising for NPCs in asteroid belts "ratting". And not just because of the Fun With Abbreviations to be had with pieRATe...player pirates don't get called that.
Krusty's Fun House is an entire game about exterminating rats.
In Eternal Sonata, while there's a tiny part of the game before it, Allegretto and Beat's first battles are in an Absurdly Spacious Sewer with a lot of rats in it. The only ones you're required to fight, however, are the ones in the bottleneck that serve as a combat tutorial for item use, Special Attacks, and light levels, should you elect to let it be one, and the boss and entourage at your destination.
In Mother 1 you have to enter your basement towards the beginning of the game to retrieve a certain item, where there is a chance that you will fight rats.
Any time you start out on lower levels in Dungeons & Dragons, you will be killing rats. Just like starting in a tavern. More recently, goblins are becoming the staple of low-level adventurers, but they're not a big step up.