Generally considered to be where Akane Tendo draws her Hyperspace Mallet from in Ranma ½. Mousse's fighting style revolves around this trope — he secretes impossibly large amounts of junk about his person and then whips various bits and pieces out to use as weapons as he needs it. This is played up in the anime, where Mousse has pulled out such weapons as: eight katanas (wielded 4 in either hand) at once in the first Non-Serial Movie, giant tops with razor-bladed edges, and a massive bomb bigger than he was (promptly lampshaded by Ranma, who pointed out there was no way Mousse could possibly have been hiding something that big). His favorite appears to be a swan-shaped training potty with which he smacks his opponents in the face.
Mousse even manages to hide weapons as a duck, producing them from under his wings instead of his sleeves. He's quite insistent during his introduction arc that there's nothing magical about his skill, though.
Lum from the Urusei Yatsura anime starts using a large mallet on Ataru starting around episode #110, possibly to break up the monotony of electrocuting him.
When the author of Hellsing was asked where Anderson takes his bayonets from, he answered, "From the fourth dimension of course."
In Gundam Wing: Endless Waltz, Wing Zero drops into the sea with a beam saber after fighting Wufei in the atmosphere, having been picked up in space carrying no other weapons. When we next see Zero, the suit is hovering in the sky, aiming at the Presidential Shelter with its twin buster rifle.
The manga version tries to explain this by showing the rifle mounted on Zero's backpack in a few scenes; this doesn't line up with the anime, but it's still an explanation.
It has a few moments early on where Jessie, James, and Meowth seemingly produce weapons, pulled-from-nowhere Hammers, and other items to which they likely wouldn't have room for in their uniforms (which don't seem to have any visible pockets, except for James's pants). This, however, does not apply to Poké Balls, which have been shown on-screen to change size for storage in pockets or on belts.
The Poké Balls themselves, on the other hand... Once a Pokémon is caught, it can be used to carry that Pokémon, regardless of the Pokémon's size or weight, even a Pokémon the size of a Wailord. (There's even a type of Apricorn Poké Ball called a Heavy Ball that specializes in catching large and heavy Pokémon.) This is naturally explained by technology on the subject, although there are hints that there were magical versions of devices used to hold Pokémon centuries ago.
The backpacks, which are not very big, but contain anything from large food supplies to camping tables to sleeping bags and even an umbrella (in Mewtwo Strikes Back, for example).
In the manga Cafe Kichijouji, during Jun's Berserk Button moment, he picks up a large rock to crush Maki with, who in turn shouts, "Where did you pull that natural boulder from?!"
In Dragon Ball, Bulma does this more than once to punish Roshi for his perverted antics. Lunch also does this in her evil mode, but with machineguns.
There's also the time where, after escaping from an abandoned pirate hideout, Bulma reaches into her bikini bottoms and pulls out an impossibly massive diamond. Take that as you will.
Doraemon's four-dimensional pocket. It's shown to be larger on the inside and can store all manner of things including a telephone booth twice as tall as Doraemon.
Akazukin Cha Cha had a small brooch during the final third of the series which could carry around things in it such as ice skating boots.
Sousuke of Full Metal Panic!! fame somehow manages to keep a huge arsenal on his person, much to the dismay of his classmates, teachers, and enemies. Kaname also has a paper fan she pulls out of hammerspace to punish Sousuke with when he goes too far.
In a Beach Episode Kaname even produces one while dressed in a skimpy white bikini.
Shown in one particular episode in which he is commanded to drop all of his weapons. It begins with just pistols, spare magazines and a few grenades, however after a quick time-lapse he ends up standing next to a massive pile of machineguns, rifles, and a rocket launcher.
Amy Rose in Sonic X has hammerspace for her Pico Pico hammer.
She procures it visibly after Sonic fails to return to Mobius with her. After launching a Hammer into the side of Eggman's airship's hull (he woke her up with a loudspeaker), he points out that she is unarmed. Close-up shot to the hand beside her thigh, and another Hammer appears in a puff of smoke. This happens six or seven more times, as each Hammer is launched into the airship's hull. Maybe she has Capsule Corp technology?
In Potemayo, Guchuko can carry an enormous amount of stuff in her pants. She once produces a pile of corn cobs that was taller than she was.
The Get Backers pull hammers and baseball bats out on each other from time to time. Ayamine Rando has also joked that Kazuki's bells have to be like this for him to be able to fit so much string in there... and it's the only possible explanation for where Juubei keeps his giant throwing needles, unless he stores them inside his body like Akabane does his scalpels...
Shana of Shakugan no Shana stores her flaming sword Nietono no Shana inside her cape. This is actually exactly what the cape is designed for, according to Alastor.
In the OVA, when Yuji accidentally switches bodies with Shana, Yuji and Shana put a large portion of what appears to be a junk yard of sorts into her coat.
Hayate the Combat Butler subverts this at least once with Sakuya's fan. True, it seemed to come out of nowhere, but afterwards she folds it up and sticks it into a pocket on the inside of her jacket.
The point of Trace Projection magecraft in Fate/stay night as used by Archer and later Shirou. When using this magecraft, Archer crafts and stores analyzed weapons inside of his Reality Marble, and summons the copies into the real world through his own body when needed. Similarly, Gilgamesh's Noble Phantasm is a portal to hammerspace that he uses to summon his belongings — often at high speed.
Sanzo of Saiyuki keeps a fan somewhere on his person which apparently is meant only for beating the snot out of Goku and Gojyo when they get too noisy for Sanzo's liking.
The One Piece manga recently showed off Blanmenco, the 6th division leader of the Whitebeard Pirates, whose Devil Fruit power seems to be pockets on his body out of which he can pull anything. To drive the point home, the item he pulls out in battle is a hammer bigger than himself.
Another example comes from a 20-second bit of filler in Impel Down. When first starting at the prison, Hannyabal is tricked to turn his back by a sexy female pirate named Olive, who then bashes him over the head with a giant hammer.
Garp somehow manages to take out a humongous iron ball that's larger than the very battleship he is standing on.
What, no glory for Pauly? Without the power of a Devil Fruit, he must have a lot of Hammer Space for the massive quantity of ropes he uses as weapons.
Mahou Sensei Negima! is required to include this trope. Many cases are actually justified as being magical constructs, such as Asuna's sword. But of the rest...
Kaede's shurikens, which are over six feet from tip to tip! Her classmates (and other folks) often wonder where on Earth she was carrying the things.
Her pactio artifact is a cloak that contains a whole house in it and makes her invisible, being utterly pointless as she is already a master in that. But having a portable Clown Car Base does come in handy.
Fushigi Yuugi gets bonus points for doing this in an environment reminiscent of Ancient China. Items include sunglasses, a rake and a bullhorn.
Sana from Kodomo no Omocha has a yellow and red rubber hammer she pulls out of nowhere to hit people, usually Akito. It varies in size, from one the size of her hand to one bigger then her body. Her mom has one too.
Hitagi Senjougahara from Bakemonogatari carries more office supplies in her schoolgirl uniform than one could fit in a reasonably-sized crate, and most of the supplies are awfully pointy, as well. It's probably best not to pry into where she keeps them, or she might demonstrate what they're used for.
In Fairy Tail the mage Erza Scarlet has a nifty example of this, she can actually pull multiple weapons and armor from some weird personal dimension. The various gear-sets generally have specific amplifier enchantments.
In Naruto, objects can be stored as kanji on special scrolls. The evil medic Kabuto keeps a collection of bodies (eww) on such a scroll, and Tenten's fighting style centers around producing stored weapons this way.
The space provided by Kamui, a Mangekyo Sharingan ability, has been put to creative uses by Uchiha Obito, such as for storing weapons, sharingan eyes, captured enemies; performing surgeries, etc.
Yu-Gi-Oh! The Abridged Series lampshades Yami Marik's ability to produce his Millennium Rod artifact out of the air through the explanation "Now I'm going to use my Millennium Rod, which I keep clenched between my buttocks, to send this duel to the Shadow Realm!"
Luna from Sailor Moon: All those transformation items, disguise pens and magic computers she produced from thin air. And Artemis in the Sailor V manga.
In early episodes, we see her do an aerial somersault and produce some in a flash of light. Hammerspace is probably the best explanation for where the Scouts keep their wands, Ami's computer, and Usagi's Pen and various wands and sceptres. Tux seems to produce roses as a power.
Actually, any transformation power could qualify — where do your normal clothes go when you're in a mystically-armored fuku?
Akiharu: Where did you pull that gigantic sword from in the first place?
Hadyeh: Please don't ask such embarrassing things.
Maka from Soul Eater occasionally pulls a book out of Hammerspace to hit people with.
A VERY large book.
Also, Shinigami-sama's hands.
Revy from Black Lagoon: Even while wearing a belly cut sleeveless top with extremely short denim hot pants, she still manages to pull spare magazines out during any one of her number of shootouts, and I'm pretty sure her pair of shoulder holsters don't have infinite pockets on the sides. Even when she's dressed more practically during the Yakuza story arc (skirt, winter hose, and a long sleeve winter shirt) the location of all her magazines remains a mystery.
Yu-Gi-Oh, season 0 (The Shadow Games). Yami Yuugi frequently pulls out random (or illegal, or in illegal amounts) objects that would be rather impractical to carry around:
Episode 1: he makes appear a rope of decent length and two decks of playing cards, as well as tape, and tapes one to the spire of a building in milliseconds.
In a later episode, he not only pulls out several bottles of chloroform, but a considerable amount of wire and some sort of pins, as well as strings the chloroform bottles from the ceiling and pins the wires to a clock in milliseconds.
Hanaukyō Maid Tai La Verite. Fiery Redhead Ryuuka can pull all sorts of weapons (including pistols, hand grenades and assault rifles) out of nowhere, as she proved in one titanic battle with a Humongous Mecha created by Ikuyo Suzuki.
In the first part of the ninth episode of Panty & Stocking with Garterbelt Panty, Scanty and Kneesocks manage to pull their weapons out of thin air despite being in swimsuits, and therefore having no panties or knee socks to transform into weapons.
In Axis Powers Hetalia there have been multiple times where characters have pulled objects out of nowhere.
In Haiyore! Nyarko-san, no matter where he goes, Mahiro Yasaka always has a fork handy for when Nyarko, Cuuko, and (rarely) Hasuta get out of hand; we later learn it's a skill he inherited from his mother Yoriko, and she's actually even scarier with them than Mahiro. One episode shows Yoriko wearing bandoliers of forks all over her body, but this is a Shout-Out to Kamen Rider Eternal rather than an justification.
Episode 9 of the second TV series establishes that the forks are mundane in origin by showing Mahiro getting them in bulk from the dollar store.
Lupin Family All Stars shows Goemon sitting crosslegged, in nothing more than shorts and a tattered jacket. He pulls out the Zantetsuken from his hair?