Generally, this trope applies to varying extents to most tabletop RPG groups, unless the players want some extra realism. The most striking example are probably the thousands of gold pieces which the characters acquire during numerous adventures. There is no possible way a human could carry them all at once due to the sheer weight, but they seem to be always at hand for any possible transaction. Actually, rulebooks usually provide information on the weight of a gold piece and suggest that characters would store their fortune in even more valuable assets like magical items, gems or pieces of art, but this is usually ignored since most players feel it would needlessly slow down the pace of the game.
In fantasy settings, the player's horses often seem to pop up ready to take them to the next location, quest, etc. no matter how improbably they would have been there or how even the players got them there. Some GM's are more sticklers about it, but many handwave/ignore it simply for convienence sake to move the plot along.
Players almost always seem to have their weapons, armor, etc. at the ready, no matter what they were doing before they needed them. As above, many games have spells and special items to explain this, but often it's just accepted they sleep, bathe, attend royal banquets, etc in full armor with their sword, dagger, bow and quiver, and handy bag of magical items.
Toons can store up to eight items in their 'Back Pocket', whether that item is a box of paper clips or an anvil.
Sadly, with the advent of 4e, the Portable Hole is no longer any form of Hammerspace, it's simply a portable hole. You apply it to a surface, and it makes a hole in it. You take it off, the hole goes away. You can't store anything in them any more.
The 1st Edition "Deeppockets" spell allowed this trick for a day or so, using one's garb. All these things are safe only until someone tries to stuff them into each other, though.
Heward's Handy Haversack is an especially iconic variant; in addition to being a Bag of Holding, it's also enchanted so that whatever item you reach for is always on top, so rather than rummage you can literally just reach behind your back and produce whatever you need, cartoon-style.
Exalted has an extradimensional un-space known as "Elsewhere." There are several Charms that allow the Exalted to store their armor or weapons Elsewhere and recall them at a moment's notice. A comic in one sourcebook has a mad inventor create a device that will take him Elsewhere, so that he can steal everyone's unguarded valuables... only to find out when he gets there that he can't move. note He appeared as a background gag in Keychain of Creation when Marena was explaining Elsewhere to Secret. The title of that page was even "Check Oadenol's Codex," which was the sourcebook mentioned above.
The roleplaying game Tales from the Floating Vagabond has the Trenchcoat Schtick, which operates in the same way for small and medium items, but only if someone says something along the lines of "Oh, if only we had [insert name of small- or medium-sized item here]!"
Warhammer 40,000 even manages to make this trope horrible with the Obliterators. Chaos Marines (most likely former Techmarines) are infected with a virus from the Warp, which already has Really Bad Idea written all over it. As a result they are not only permanently fused to their armour and weapons, but can spontaneously spawn any weapon they desire and an infinite ammunition supply for the weapon, including-but-not-limited-to the ammunition-devouring Assault Cannon and the massive Lascannon. The entire experience is noted as being exceptionally painful.
Also, when Lucius the Eternal is killed, his killer is transformed into Lucius, somehow also obtaining his armour and weaponry.
One of the Maid Powers in the AnimesqueMaid RPG is Weapon From Nowhere, which lets your maid PC make surprise attacks by pulling her weapon out of nowhere.
In Nomine supplement Superiors I: War & Honor. The Archangel Laurence's Servitors have an Attunement called "Scabbard" that can hold an unlimited number of personal weapons.
Orpheus has the Beckon Relic ability for Wisps. It allows them to reach through a dimensional tear and pull out an item that they must concentrate on; the catch is they don't get to chose exactly what comes out. For example, if they think "gun," they may get anything from an AK-47 to a 16th century musket.