The "pup tents" used by the wizards in books seven and eight operate similarly, except these places can be used as bedrooms.
Not quite Hammerspace but very related, in one book there's the sentient white hole that burps up random highly-ordered objects. At one point, it manages a fully assembled jumbo jet — harking to a traditional creationist argument about a windstorm in a junkyard.
Invoked explicitly in Anne Bishop's Black Jewels trilogy: Mages can "vanish" objects, presumably into their own personal Hammerspace, and call them back in when needed. The amount of Hammer Space you have directly correlates with how powerful you are.
In M.A.R. Barker's Man of Gold, set in the world of Tekumel (which was originally created as an RPG) the hero, Harsan, learns to put things into another dimension, someplace he calls "around the corner", for safekeeping. There's one catch — if you leave something there very long, when you bring it back, it is cold enough to destroy flesh. If you put an item around the corner yourself, you can get it back by concentrating on it; or you can simply grope around and bring something back that someone else put there. But you won't know what it is until it materializes...
In Tom Holt's Grailblazers, a character has the hereditary ability to reach vaguely behind him, and always bring the hand back holding something weapon-like.
Sycophants in the Leven Thumps series have an unlimited "void" where they stow useful stuff. Pretty annoying, it's very hard to visualize what's going on when you read "Clover fished around in his void."
Discworld dwarves have access to Hammer Space: in The Truth Gunilla Goodmountain's troop of dwarves are able to produce large weapons seemingly from nowhere.
Also, Conina in Sourcery is able to produce a seemingly endless arsenal of weapons — especially throwing knives — that she has secreted about her person, despite wearing just a simple white dress that wouldn't seem to have many hiding places. Since the retrieval of these items sometimes requires her to ask her male companions to turn away and is accompanied by a waft of perfume, we can assume that some of Conina's Hammer Space is in the form of a Victoria's Secret Compartment or its equivalent.
Rincewind's magical Luggage, in addition to being a sapient travel accessory with a hundred legs and a mean temper, also appears to have limitless interior. It has "eaten" more than a few enemies and has served as a hiding place for Rincewind and others when bad guys are around. It also carries clothes, especially Rincewind's underpants, which are always freshly laundered and neatly folded when he asks the Luggage for them. Definitely qualifies as a Bag of Holding, too.
Victor from Moving Pictures uses this trope to justify this trope, when he summons a horse and sword from nowhere by tapping into the ambient effects of Holy Wood magic. Film characters are always pulling weapons and equipment out of nowhere when needed, and film audiences accept it, hence it's fully within his power as the Discworld's top film star, provided he plays out such deeds in character.
The wizards of Discworld have a lot of artifacts that can access Hammerspace, including a cabinet which, if you can find the proper drawer, contains anything you can think of and quite a few things you probably couldn't. This includes their own clothes: "You could find anything in a wizard's pocket - peas, unreasonable things with legs, small experimental universes, anything..." Lords and Ladies
In The Guardians, Guardians and demons have "caches" to which they can vanish and retrieve items. Younger Guardians that grew up playing videogames actually call it a hammerspace.
In Ciaphas Cain, HERO OF THE IMPERIUM!!!, Jurgen's webbing and greatcoat seem to contain an infinite amount of ration bars, tanna, and various helpful objects like goggles.
In Brandon Sanderson's The Stormlight Archive series, Shardblades automatically go into Hammerspace when dropped or otherwise separated from their owner, unless he or she wills otherwise when releasing them. The owner can resummon the Blade at will. This is a necessary feature as they are both really huge and incredibly valuable. This feature ensures that you have to kill somebody to take the Blade against their will and seeing as said Blades are able to cut through all normal armour effortlessly, and kill anything in one hit to boot...
In Harry Potter and the Deathly Hallows, Hermione uses the magic Hammerspace spell (an 'Undetectable Extension Charm') to put a ton of books and other stuff into her beaded purse. Including a large picture frame, which is larger than the purse itself. Amazingly enough, it isn't heavy to her at all (though the things inside aren't immune to breakage due to shaking the purse around too much. It "rumbles like a cargo hold" every time it's shaken.)
In the Spellsinger series by Alan Dean Foster, an anthro turtle wizard named Clothahump has drawers that pull out of his chest that he uses to store various spell components. His house, which is built inside a tree, has a similar effect on it, though he warns that excessive use of the spell can become very expensive because it causes inflation.
In the Death Stalker series, when Owen travels back to the mythical First Empire, he discovers that wealthy people of the time can buy bodies just like clothes. These bodies are stored away in subspace and be donned in a split second. You can have bodies for riot control, combat, courtly occasions, sex, etc.
In a Doctor Who Expanded Universe novel, the Doctor lands on a planet which follows cartoon rules and is inhabited Expys of many well-know cartoon characters. Towards the end the Doctor uses the rules of the world to produce a custard pie gun (an appropriate weapon for the Doctor) from Hammerspace to disable the bad guy.
Zed from The Sword of Truth series has a wizards closet, though it is only mentioned once, early in the first book.
Caroline, from Tunnel in the Sky, leaves for her off-world survival test unarmed, barefoot, and with an overnight bag. About fifteen minutes later, Rod arrives in the relay room and sees that she ditched the bag before leaving. A month later, Caroline arrives at the fledgling colony with all of her odd items, including her diary and a saucepan. Nobody is sure how she kept and carried it all without a bag.
In Mike Leon's Supervillainous!, the main character, Baron Hammerspace, has this as a super power. He can store and retrieve anything he wants in his jacket, provided it is not too big to wrap the jacket around. He seems to have an infinite supply of guns, bombs, and bizarre science fiction weapons in there.
The Fablehaven series has the transdimensional backpack with a storage room inside.
In ""Emily The Strange The Lost Days'' Emily/Earwig's dress has pockets that can hold an inordinate amount of items, cats included. However, it was never properly used and only mentioned as a curiosity.