Code Geass: In season two the Black Knights take refuge in the Chinese Embassy in Tokyo, and even claim one of the embassy's rooms as their sovereign territory. The embassy's smack dab in the middle of territory controlled by the vastly, vastly superior Brittanian military; the only reason Brittania doesn't just attack the Black Knights is because invading a foreign embassy is enough of a diplomatic faux pas that it'd probably just start another war. Bit of an unusual example, though, in that the Black Knights can apparently escape unnoticed any time they wish, but prefer to keep the Brittanians distracted by the embassy for as long as possible.
Saving Private Ryan: Uses this trope in the climax. Outnumbered and outgunned by advancing German forces, Miller and the rest of his squad put it all on the line for the survival of just one man.
300 pivots around scenes were group of greatly outnumbered heroes holding off a vastly greater number of enemies.
John Woo's The Killer features one of these as its final shootout, with the title character and his Cowboy Cop ally defending the Killer's last place of sanctuary, a church, against a virtual army of assassins sent by his ex-boss to murder them all.
Small Soldiers had a siege near the end.
Scarface ends with a siege by assassins working for Alejandro Sosa against Tony Montana's mansion, which doesn't really get going until Tony takes up an M-16 with a grenade launcher with a cry of "Say hello to my little friend!"
The Siege, usually involving a Town Boss being held in a city jail, was the climactic event of four John Wayne movies, including Rio Bravo, El Dorado, The Sons of Katie Elder, and Rio Lobo. Apparently Duke liked this story line even more than he liked stalking and spanking beautiful women (three different movies!).
Used twice in The Lord of the Rings, first at Helm's Deep, then again at Minas Tirith. Both times, the siege is broken when The Cavalry arrives... literally.
Also shows up in The Hobbit when Thorin and his band are holed up inside the Lonely Mountain as the armies of Laketown and the Wood Elves try to get in to claim the treasure.
Dan Abnett's entire Warhammer 40,000: Gaunt's Ghosts novel Necropolis is one prolonged siege battle, with the Chaos-corrupted hive city Ferrozoica hurling their entire population at the much larger but much less-militarized hive city Vervunhive. Think Minas Tirith, but with tanks and a good hundred times the manpower. It occurs again in Sabbat Martyr, with Gaunt explicitly comparing and contrasting the two situations, noting that this second time around the "good guys" were even worse off.
Also in the game background the Ultramarines' defence of their polar fortress againt the Tyranids that had invaded their home planet. Most of their 1st company died holding the place untill the Imperial Navy could drive off the Hive Fleet by having a battleship perform a Heroic Sacrifice and explode it's warp core right in the middle of the fleet.
Noticeably averted in War and Peace. Kutuzov abandons Moscow despite everyone on his staff and his emperor demanding that he hold Moscow against a siege.
A mainstay of Henryk Sienkiewicz's ''Trilogy'', set in the 17th century Polish-Lithuanian Commonwealth. Each of the books in the trilogy has a climactic siege featuring the defenders fighting against great odds.
Rogue Male: for a large part of the story, the hero is besieged alone in his hideout, which has gone from a refuge to a hellish trap.
The entire premise of Legend by David Gemmell: the garrison of the fortress of Dros Delnoch must hold on against the Nadir army to buy enough time for their country to levee an army. Most of Gemmel's books will end with The Siege and/or Last Stand
In the book Azincourt by Bernard Cornwell it goes into great detail over the siege of Harfleur. The siege is a shambles, the British end up with dysentery, the French keep rebuilding the walls and to top it all a ship gets past the blockade to resupply them. When King Henry V finally takes the small town he lost so many forces he can't possibly hope to defeat the French in open battle but to save face forces his men to march around France attempting to avoid their army...that doesn't work out so well.
Colas Breugnon has a siege described early in the novel. Even though a few people die, both sides come to an agreement after a few days and settle down to eat together. No one's very sore about the entire incident.
In The Power That Preserves (the third book in the Chronicles of Thomas Covenant series) Lord Foul's army of monsters does this to Revelstone.
In Mistborn: The Well of Ascension the protagonists are besieged in Luthadel by three armies at once; the fact that the besieging armies are all working against each other is the only reason Luthadel lasts so long.
In Mistborn: The Hero of Ages, the good guys are the ones doing the besieging, until the Big Bad's army shows up and the besiegers and the besieged decide to team up.
Occurs several times in The Malazan Book of the Fallen, most notably the exceptionally one-sided siege of Capustan in Memories of Ice.
The first series of the revival ended with a Siege, though it was slightly subverted in that the good guys did not actually end up holding off the evil Daleks, and by the end of the episode, every main and minor character, with the exception of Rose Tyler, was dead. Two getbetter.
"The Base Under Siege" is a standard Doctor Who plot ("Moon base, sea base, space base, they build these things out of kits!"), especially in Pat Troughton stories, such as "The Wheel in Space"
"The Waters of Mars" subverts a number of conventions in this regard.
"Heart of Gold", in which the crew defend a whorehouse from an evil tycoon.
In Serenity, defending Mr. Universe's hideout against Reavers so Mal can use his broadcast equipment.
Stargate Atlantis: The first-season finale, named appropriately enough "The Siege", shows the main characters defending Atlantis from a Wraith assault.
Most TV series set in war zones, and many western series, eventually use this plot.
Deep Space Nine: "The Siege" (natch), "Way of the Warrior", and others. Since the setting was a station, this was a natural plot idea. Speaking of which...
"Siege of AR-558" (not to be confused with the above episode) is particularly gruesome.
Andromeda: "Last Call At the Broken Hammer", "Its Time Come Round Again", "The Dissonant Interval" (they don't exactly win those last two).
24: At one point in Season 4, Jack Bauer and three civilians must hold a sporting goods store against a squad of heavily-armed commandos until help arrives.
The first episode of Kaizoku Sentai Gokaiger has all the past sentai teams defending Earth from an alien invasion.
In the season 4 finale of Burn Notice, Vaughn's entire organization corners Michael and crew in a half renovated hotel. they get out when Sam convinces congressman Cowley to call in the army to save them.
Many of the scenarios in the board game House on Haunted Hill are variations on The Siege with different Monsters Of The Game.
Videogames
Too many First-Person Shooter and Real Time Strategy to list. Usually includes a timer to let you know exactly when the defending stops and counter-attacking starts. The entire Tower Defense subgenre is built around this.
Happens in Neverwinter Nights 2 when the hero's castle is besieged by the undead army of the King of Shadows. The already problematic odds take a turn for the worse when one of the hero's companions turns out to have betrayed them by sabotaging the gate and when the undead, including the vampires, turn out to be unaffected by sunlight.
Mass Effect 2: Garrus' recruitment mission and Grunt's loyalty mission both consist of three or four heroes holding a somewhat defensible position against a horde of mercenaries/alien monsters, followed by a Background Boss. Legion's loyalty mission is a sort-of Tower Defense scenario.
Urban Dead: The game revolves around humans building barricades inside buildings and zombies trying to break in. Most famous is propably Second Siege of Caiger Mall, going for three real life months.
Goblin sieges in Dwarf Fortress; more rarely, human and elven sieges. If all the resources you rely on are subterranean (water, magma, farmlands, wood, ores,) a virulent forgotten beast can effect a siege from below.
Webcomics
In Order of the Stick, Azure City, a bastion of good partially ruled under the watch of paladins, is attacked by a massive army of hobgoblins led by Redcloak, an evil goblin cleric and Xykon, an evil human lich sorcerer. The protagonists find themselves defending the city alongside the paladins. The good guys actually lose with heavy casualties, including the leader of the protagonists. A very, very long arc was dedicated to the fallout of the battle, including the only recent resurrection of said leader.
The first two-part season finale appropriately enough entitled, "The Siege of the North," has the main protagonists aid the Northern Water Tribe in staving off a Fire Nation assault.
"The Northern Air Temple," wherein said protagonists defend the titular temple... from a Fire Nation assault (the Fire Nationdoes a lot of assaulting). Also, Iroh's legendary six-hundred day Siege of BaSingSe.
This trope is a case of Truth in Television. Sieges have been and remain a common military strategy and a good number of movies and television programs base their siege plots on real life sieges like Leningrad and the Alamo.