Dungeons & Dragons veterans will often remember taking ten-foot-long poles with them, just in case they ran into a trap where the switch is ten feet away. Mean-spirited DMs would make the switch eleven feet away, which would lead to players pointing out that their arm added an extra foot. So the next switch would be twelve feet away, naturally.
Spoofed in game designer Greg Costikyan's novel Another Day Another Dungeon, in which one of the main characters explicitly takes a collapsible eleven-foot pole into dungeons for precisely this reason. One wonders if his world's GM started making twelve-foot traps in response. The sourcebook Dungeonscape adds a 12 ft collapsible pole.
This is almost certainly the reason for the Munchkin card game (and Munchkin d20 books' equipment list) including an eleven-foot pole (aside from sheer one-upmanship on the poor deluded fool who brought a ten-foot one).
Both of the above are "ten-upped" by a D sourcebook which actually contains a 21-ft collapsible pole.
Other items typically carried by adventurers in 3.5th Edition, largely because they're cheap, include rope, chalk, signal whistles, mirrors, fish hooks, and sewing needles. Crowbars, shovels, hammers, pitons, and tarps are slightly less common due to their weight.
Among 3.5 gamers, the 50 feet of silk rope is the new ten foot pole in terms of iconic adventuring gear. It goes back long before 3.5, though. Rope has been a vital part of every adventurer's kit since the dawn of the game. When Sam Gamgee in The Fellowship of the Ring muttered to himself "You'll want it, if you haven't got it," millions of adventurers nodded in silent sympathy.
The 10-foot pole is referenced in this strip of The Order of the Stick. note Xykon also showed himself to be this trope by having researched "Xykon's Moderately Escapable Force Cage" well in advance, to convince a paladin that she'd escaped on her own.
One of the adventurers in the Adventurer's Club in Neverwinter Nights 2: Storm of Zehir goes over a checklist that includes a ten-foot pole.
The Pathfinder Chronicles campaign setting includes a prestige class with the ability "Deep Pockets." This ability allows the character to "carry up to 10 pounds of unspecified equipment worth up to 100 gp." This equipment can be any non-magical gear "that can reasonably fit into a backpack."
Dread Fangs of Lolth get an ability that always lets them act in a surprise round. Always. God help you if you try to ambush a Dread Fang of Lolth, as you'll probably discover that he spent the last 10 seconds stabbing you For Massive Damage without you noticing.
Wizards and clerics (and some other classes) also need to be crazy prepared for every situation, because they have to prepare their spells in advance. In most cases surprised (unprepared) wizard = dead wizard. If they are prepared, though, you may quickly find that time suddenly stopped and the wizard in question blasted you with 5 or 6 spells that could utterly annihilate you alone, not to mention any resistance lowering or protection breaking. A fight between 2 high level mages is practically decided by the measures they took to be able to fight spellcasters.
A lot of famous villains in the game are described this way. Probably the uber-example is Dispater, the ruler of the second layer of Hell. He is described as "the living embodiment of caution". He rarely lives the Iron Tower, his stronghold, which makes him nearly invincible, has a network of spies that is second only to that of Asmodeus, and has half of his servants closely watching the other half, and vice-versa. He is known to always have at least four contingency plans and backup plans to every one of his schemes, and most of them take years, if not centuries, to come to completion, as he never rushes any of them.
In Paul Kidd's novel adaptations of several classic adventures (White Plume Mountain, Descent into the Depths of the Earth, and Queen of the Demonweb Pits), the heroes are plagued by an enthusiastic wannabe-adventurer teamster sidekick who constantly pesters them with "advice" on how they need every little piece of contingency gear that Player Characters are infamous for carting around. The heroes are a certifiable Bad Ass and a powerful wizard pixie (who can fly, obviating a lot of traps right away), but every once in a while the wannabe is proven right.
This is a time-honored tradition in roleplaying games, starting from the first editions of Dungeons & Dragons. Many games have even begun giving explicit Crazy-Prepared kits in a character's starting equipment (Chill, GURPS 'personal essentials', HARP, et multiple cetera).
In ANY tabletop RPG, someone has a loadout with blunt, slash, pierce, fire, cold, possibly ice/pure magic/acid, and throwing weapons in case their main loadout doesn't have reach. It's like Medieval More Dakka.
The Space Marines of Warhammer40000 are improved by genetic engineering. Very extensive genetic engineering. As in, they can darken their skin to resist radiation, go into suspended animation to await help from being afflicted with likely mortal wounds, have a massively heightened sense of taste to be able to detect individual chemicals within what touches their tongues and spit metal-corroding acid among other changes more normally tailored toward the purposes of front-line combat.
GURPS has an advantage called "Gizmo" that lets you carry one or more useful items, specified at the time you need them.
Spirit Of The Century has this in the form of the Universal Gadget stunt. Alternatively, you can take the Rare Artifact stunt if you want something magical and with more features, though this does have a down side.
Toon also has Gizmos, although these are statistically more likely to be anvils or sticks of dynamite than anything else.
In Mage: The Awakening, mages are described as being at their most formidable when they are able to prepare their powers in advance, and are rather more vulnerable than other supernaturals when caught off guard, and there can be quite a diverse number of beasties in the New World of Darkness. Thus, any successful mage will take the idea of being Crazy-Prepared to heart (particularly the Adamantine Arrow, whose creed includes the phrase "Adaptability is Strength)". This is especially true in mages' interactions with one another, since it means needing to be Crazy-Prepared against dozens of others who are also Crazy-Prepared.
Truly magey mages will take it to the next level by adding mid-level time or fate effects to their spells, allowing them to outright try to second-guess the storyteller with spells that when a particular event occurs or a particular potential target approaches, such as teleporting them to the hospital if they're rendered unconscious or banning anything made of lead or steel from entering their hotel room in gang territory. This has evolved into a second game for some players, where the player writes their conditions on a card that's only revealed to the storyteller after they've developed their own counter-strategy.
Changeling: The Lost has a similar arrangement. While changelings don't have the universal adaptability of magic that mages do, what they do have are Catches — specific conditions that allow them to use their magic without having to pay for it. A battle-hardened changeling might bring a torch, a golden chain, a friend with red hair, a fish's eyeball, and the name of a firstborn son with them to a melee just in case they need that special edge.
The core game has The God Machine who uses Rube Goldberg conspiracies like planting a slight mechanical defect in one specific car because years later one of his enemies will use that car to escape his grasp and the defect will kick in at that specific time.
The DC Heroes Role-playing Game (which became Blood of Heroes after losing the license) had "Omni-gadgets," pieces of equipment bought during character creation whose abilities weren't determined until they were used, to simulate a character who "just happens" to have brought exactly what he needs. Every omni-gadget had a letter code from A through D that determined what abilities it could simulate (e.g., "Type A" gadgets could simulate physical abilities like strength (a crowbar, say) or Body (a bullet-proof vest) while ABCD gadgets could do almost anything). So a character with five ABCD Omni-Gadgets could reach into his utility belt and pull out anything from a flamethrower to a personal teleporter (which he put there for a situation ... just like this!) five times per adventure.
The (W)Hole Delver's Catalog by Task Force Games is a humorous catalog of innovative gear for adventurers who want to be Crazy Prepared. Examples include The Cutting Edge Shield, an Inflata-Demon, a Medusa Cap, the Two-Way Armor, the Droopy Sword, and the Portable Hoist.
Speaking of Task Force Games, Starfleet Battles includes a type of ship known as a Police Flagship. These typically include scout sensors; mine sweeping, ground assault and heavy transport shuttles; and repair facilities (of the kind normally found on dedicated repair craft), in addition to some dedicated cargo space and extra marines. The only shortcoming they have is...in actual combat, they get curb stomped because they've got no heavy weapons.
Exalted has paranoia combat, which consists of the logic "something arbitrarily bad could happen to me at any time - as soon as I'm in combat I need to use this combo that makes me pretty much immune to harm as long as I have motes, every action until either I run out of Essence and die or my opponent runs out of Essence and dies". The most extreme paranoia combat builds have surprise negators, shaping defences, mental attack resistance, "flurrybreakers" (you attack multiple times, they somersault over your head before your second attack), environmental damage resistance (which after a point can run for free, forever), and two different perfect defences.
Sidereal Exalted possess a power that lets them determine which of multiple options will most effectively fulfill their goals. Among other things, it could be used to know what the best choice of equipment before going on a mission is, even if they don't realise why at the time.
This is also the main reason Alchemicals learn martial arts - since they can only install a finite number of Charms at any given time, it pays to have a permanently installed repertoire of combat effects just in case, something they can only do through the Supernatural Martial Arts system (except for one other effect that allows them to install as many Charms as they like, so long as they don't mindbecoming demented sociopaths).
The Villain Iron Legacy seems to have Crazy-Prepared as his deck's theme. Literally every hero is at a disadvantage against Iron Legacy, as Iron Legacy has a counter for literaly everything.
Iron Legacy's difficulty is so high one would almost need to be Crazy-Prepared themselves and bring Heroes with consistant Ongoing removal, with Bunker's Alternate form Engine of War being a good choice due to Ongoing destruction being his base power.
One of the sample Madness Talents in Dont Rest Your Head is "Preparedness". They describe it as being able to be supernaturally prepared for whatever it is that you might have encountered, up to and including retroactively having written down random numbers on a slip of paper and putting it in to your pocket that just so happen to be the combination to open the safe that you need to break into. Needless to say, abusing causality to that effect can have some minor reprecussions...
A version of this appears with the Resourceful Pockets trait in Rocket Age. You have pockets, a bag or some other container. Its full of stuff that you can just reach in and grab with no explanation as to why you would have it.