There were thousands of Medieval Castles, many of which never were besieged, so trying to determine which castles were the hardest to besiege would be very difficult.
One feature which made a castle hard to take by assault or siege, was to build it on an island. It was hard to get troops up to the walls to assault a castle on an island, and it was also hard to starve a castle into submission if boats could re-supply the castle. Even if the besiegers had local control of the sea, a storm could always drive their blockading ships away and let re-supply boats sneak in.
An example of a castle on an island is Mont St. Michel in Normandy.
According to legend, the Archangel Michael appeared to St. Aubert, the bishop of Avrances, and instructed him to build a church on this island.
(I did not mention the key castle defense of having Archangelic protection for your castle, but it may have been the best defense of all.)
During the 100 years war, the castle was held by the French. It was assaulted and besieged many times by the English, but managed to resist all assaults and sieges.
No castle (unless afforded divine protection) was truly invulnerable, but being built on an island made a castle more defensible than most.
Sources:
/u/mormengil has already touched on one of the defensive strategies, placing the castle on an island. Where this was not feasible, there were a number of other actions taken. As previously mentioned, the medieval period, or Middle Ages, encompassed a time frame generally accepted to begin with the fall of Rome in 476 AD and to end sometime in the 15th century. I prefer the fall of Constantinople/end of the Hundred Years War in 1453, but these are completely arbitrary dates, and others are preferred.
In the one thousand years of the Medieval Period, castle technology, defense and siege, advanced continually, from the simple earthwork and wood fortifications of the [gròd] (http://osobliwosci.eduseek.interklasa.pl/~lukasj/jpg/grod.jpg) or the Motte and Bailey, to the angled stone walls of the bastion, the precursor of which we can be see in the architecture of Saranzello Castle in Italy. That's a lot of ground to cover. So, I will instead attempt to list the various common defenses used in the period and allow you to decide for yourself what sort of castle would be most defensible. Most of this information can be found in The Medieval Fortress: Castles, Forts, and Walled Cities of the Middle Ages, J. Kaufmann and H. Kaufmann, 2001. I can't recommend this book enough if the subject interests you.
Moat Beaumaris Castle, Wales Very common to the period, unless the castle was already in a naturally defensible position. Varied in depth, but had to deep enough to prevent walking through, without being wide enough to leap over. In the 13th c, moats in France ranged between 12 and 20 meters wide, and 10 meters deep. Swimming or wading into the moat would have been incredibly disgusting, since they often acted as cesspools due to waste from the castle, human and otherwise. Later in the period double moats appear, one outside the walls, and another around the inner citadel. In the 11th c. there East/West Europe divide between wet and dry moats, respectively, but by the 13th c. most moats are of the wet variety. Assuming besiegers make it past the moat, they run into...
Enceinte This is a general term for the towers, walls, and other such defenses encircling the castle, the broadest of our categories. Many developments to these defenses migrated to Europe in the twelfth century as a result of the crusades.
Walls ranged in width and thickness dependent on building materials, but in the later part of the period, 13-15th c., masonry keep walls in Western Europe varied in thickness between 4 and 5 meters. The concept of the castle shield wall, a taller section of wall used as an enhanced defensive position was introduced at some point and grew in size to equal the height of the towers. Arrow "loops" or slits would be placed strategically, varying in form, and could be quite specific to weapon. (Seriously, this could be an entire topic).
Atop the wall was the allure, or wall walk, protected with alternating crenels and merlons. In times of siege, the open merlons could be outfitted with wooden firing embrasures, a swiveling, shutter-like apparatus with an arrows loop in the center. Temporary roofs could also be added, wood laid over with animal skins or other non-flammable material. Prior to the 12th c., wooden hoardings could also be constructed to increase firing range and allow defenders to fire down on attackers more easily. There is some debate as to whether or not hoardings were permanent, as of yet unresolved. After the 12th cent. hoarding are replaced by machicolation or the bretèche. Not to be confused with garderobes, which look very similar, but are actually bathrooms. Placement usually reveals which it is.
Towers varied in shape by the architect's taste. There were generally four categories; the corner tower, mural tower and recessed mural tower, and flanking tower. The mural tower is the conventional image, while the recessed simply juts out less. The flanking tower was placed near gates or other desirable areas to create flanking fire and to eliminate blind spots at the base of other towers. Square towers were more vulnerable to mining, so in the 12th c., styles moved toward circular or semi-circular varieties. Towers could be closed or open in the rear for easier access to unconnected floors. Aside from firing loops, there would be no decorative openings
Plinth Provins Castle, France The angled section at the base of walls and towers that acted as a counter-mining measure. It also made stones or other items dropped from the battlements to bounce into attackers.
Gatehouses Malbork Castle, Poland Attention was paid to the gatehouse long before other fortifications, so it was one of the first to be made of stone. There would be at least one portcullis, wood or metal, made to raised, or later swiveled, out of the way. This would in addition to multiple conventional "gates," large, wooden, metal-reinforced doors. The main gate would be flanked by towers leading into a narrow tunnel. Inside the passage, the walls and roof would be lined with arrow loops and murder holes. The floor might also be rigged to collapse or be retractable wood in some sections. To prevent ramming, the passage openings were often placed at angles to the towers, and in some cases, a singular barbican was placed outside the walls for the protection of the gate or path to the gate and was connected to the castle by a long walled road. In some cases the barbican was placed above the gate.
This covers the majority of defenses you'll see in the typical castle. Going over them always reminds me why besieging a castle was no small feat. It was quite the arms war. After the advent of better field artillery, castle walls got shorter as profiles were decreased and they were replaced with star forts.
Hope this answers some of your question.
One of my personal favorite castles is the Crusader fortress of Krak de Chevaliers. It was never taken by force, was eventually only captured by treachery. It is an excellent example of the medieval European use of castle construction to defend and consolidate contested territory.
Some interesting defensive devices include:
The gate to the keep not being in line with the gate to the curtain wall, meaning you had to walk under the walls with crap being thrown and shot at you to get there.
Barrel vaulting, making the fortifications themselves incredibly strong. In the recent civil war, Krak de Chevaliers seems to have survived rocket and artillery attacks relatively unscathed.
Position: the castle is constructed on a steep hilltop, and the gate is built significantly above ground level, accessible only by a ramp
Broad lower walls, making sapping attempts relatively pointless.
Daulatabad is one of the most elaborately defended forts that I have come across. The fort had a large moat and three concentric walls protecting the keep. The keep itself sits on a 656 feet high (200 meters) high rocky hill the lower portions of which were hewn by hand on all sides leaving 164 feet (50 meters) high vertical stone cliffs completely surrounding the "keep".
To access the keep, after crossing the concentric walls, one had to navigate a system of tunnels and cross a wooden bridge suspended 65 feet (20 meters) above the moat.
The fort was considered impregnable until the advent of cannons.
This post by /u/hoohill does a great job showcasing this feat of medieval engineering with a lot of descriptive pictures.
Even though it wasn't an actual castle, the Walls of Constantinople where impregnable when properly manned. Each one of the towers on the main Theodosian wall was the equivalent of the main tower from an average castle at the time, and there where 96 of them. So even if a besieger could penetrate the trench, moat and the outer wall they still had to take each tower, one by one. These walls where the main reason the Byzantine Empire survived for over 1000 years after Rome fell. The reason it was finally conquered in 1453 was the sheer overwhelming numbers that the Ottomans fielded, and even then it took them almost two months to take the city.
Marienburg/Malbork castle in northern Poland was also never taken by force. It was the headquarters of the Teutonic Knights, and also the largest brick castle on earth (wikipedia says it was also the largest Gothic fortified structure in Europe). It was sieged several times but to no avail. After the Battle of Tannenburg in 1410, when the Kingdom of Poland decisively beat the Knights there was a siege but the Kingdom of Poland wasn't prepared for a long siege and had to end it after 2 months. As a bonus there was very intense fighting there during WW2 between the Germans and USSR.
I'd like to piggy back on this question if I'm not too late. I was just reading about the Japanese premodern era (Tokugawa Shogunate time period). My book stated something along the lines of the Japanese and Westerners seeing eye to eye relatively well due to similar class structures and other factors. It seems like the existence of castles might strike a chord between the few allowed visitors like the Portuguese/Dutch and the Japanese…
So, were there any large differences between Japanese castles and Western castles in general?
Does anyone have any information on measurements/ floor plans/ blue prints that describe the insides of the castle and keep?
I'm interested in knowing how much room was allotted for living, storage of food and materials, and other information. Basically, I'd like to see the difference in living styles between modern (Western) houses and mansions and castles and keeps.
Also, if a castle were under siege, would it be exempt from taxes by the king?
There was the city/fortress of Badajoz, on the border between Spain and Portugal. It was a massive fortress that was rumored to be unconquerable. The French assaulted it twice in 1806 and 1809, and failed each time. It took a massive bribe to the Spanish commander to obtain the fortress.
Then the British besieged it three times, failing twice. On the third attempt the Duke of Wellington finally managed to crack it. However, it cost him a third of his besieging forces, and took a massive bombardment and three massive breaches in the wall. Wellington even wrote:
"The capture of Badajos affords as strong an instance of the gallantry of our troops as has ever been displayed, but I anxiously hope that I shall never again be the instrument of putting them to such a test as that to which they were put last night."
