I understand that it probably varied greatly across regions and periods, but I'm interested in answers from whatever area and timeframe.
I am wondering about things like:
My area/period is early medieval England, so this answer may differ elsewhere and when. This necessitates a somewhat multi-faceted answer because we have to consider three separate types of site and settlement:
One particularly pertinent contemporary source which illustrates the uses - and shortcomings - of these castles is Jordan de Fantosme's imaginatively named Chronicle of the War Between the English and the Scots in 1173 and 1174 and I will refer to it quite a lot.
Often as a result of pop history and historic or history-inspjred fantasy, we associate castles as sites of refuge for the wider population. The Siege of Helm's Deep in The Two Towers is a good example. In early medieval England, however, this is quite unfortunately not the case. 'Pure' castles, such as Corfe, Raglan, Brough, Wardour or Peveril are designed as refuges not for the population as a whole, but specifically for the local lord and his immediate retinue, and function essentially as heavily fortified private estates. In the first decades after the Norman Conquest of 1066, this was especially important for a small minority nobility ruling over a largely hostile populace. The massacre of the Norman garrison in the streets of York which prefaced the Harrying of the North in the 1080s is a stark reminder of the importance of having a safe refuge away from the majority of the population. In urban scenarios such as Wallingford, Bristol, London, Cardiff or Exeter, the castle acted often as much as inner defence as it did external.
The function of smaller, more rural castles - particularly prevalent in the Welsh and Scottish Marches - was not to function as refuges but rather, to borrow a modern analogy, as a police station or military FOB: a secure location easily defendable by a small number of men which could be used to establish control over a wide area through cavalry patrols. In the event of a war, these castles were designed to slow rather than stop the enemy, to force him to leave blocking detachments behind to contain the garrison, and allow a military response to be organised and meet him in the field. This is illustrated well in Fantosme's Chronicle: The Scottish army which invades Northern England in 1173 lacks major siege equipment and is forced to invest significant blocking detachments at border fortresses such as Alnwick and Bamburgh, and is forced to withdraw in the face of William Marshall's relief force. When it returns in 1174, a farcical attempt to storm Alnwick forces William of Scotland to again leave significant forces to encircle it, while the blocking detachment sent to Bamburgh is defeated by the garrison there. The Scottish army also takes surprisingly heavy casualties storming Brough castle even though its garrison is only a dozen knights (plus presumably attendant men at arms), and only captures Wark Castle because its defences are half constructed. When the Scottish army returns to try and storm Alnwick for a third time, this gives chance for the garrisons of Newcastle, Prudhoe, Carlisle and other smaller castles to assemble into an army which defeats the Scottish outside the walls of Alnwick and captures King William. In this scenario, the castles perform exactly as intended, and provide security to the country by means of blocking and delaying the invasion and allowing forces to be raised against it.
While the North as a whole was protected, the local populace itself was not always so lucky. It is, of course, important to remember that in an agrarian economy, killing the local populace and looting their cattle would render a war of conquest largely moot. The raiding carried out by William the Conqueror prior to the Battle of Hastings directly targeted the lands personally belonging to Harold I to goad him into battle, and the famous English chevauchees which caused such devastation in France during the Hundred Years War were again intended to goad the French into confrontation and weaken their ability to resist. On the other hand, David I of Scotland seized Carlisle during The Anarchy of the 1140s, and actively patronised the town, overseeing much of the urban development stemming from its booming silver production, but ceding it bloodlessly to Henry II of England following his accession to the throne. While the main Scottish army which marched South in 1173 and 1174 largely ignored the civilian population, not all were so lucky, and Fantosme records how highland detachments behaved with brutal savagery, looting churches, burning houses and even carrying off slaves.
In an urban setting, castles did protect the populace, but only insofar as they increased the defences of the settlement itself, and rarely as a site of last refuge. A prime example might be seen during the Siege of Antioch on the First Crusade: after the city walls fell, the Seljuk defenders withdrew to the citadel to make a stand there, but left the city's populace behind the face the ravages of the Crusaders. More beneficial incidences can be found, again, in Fantosme's Chronicle. Alongside the Scottish invasion of 1174, England also faces a Flemish invasion in Norfolk. Here, the local population flee to the city of Norwich, where they combine with the castle garrison to defeat the invading forces.
Special mention has to be made of the Anglo-Saxon burghal network. Fore-runners of the castle, burhs typically encompassed much larger sites, often incorporating open-field areas. As burhs were typically situated on major road junctions or river crossings no more than 40 miles apart, it was traditionally assumed that burhs were indeed designed as sites of refuge that were no more than a day's travel and with the openfield area designed to house refugee populations and their livestock. This model has been significantly revised following the Beyond the Burghal Hidage project given the not-unreasonable realisation that even 20 miles is a long way to travel in a day with children, livestock, the elderly and with a horde of angry Vikings on your tail. Furthermore, many of the Mercian burhs don't fit this mould. Rather the model has been revised to incorporate burhs as focal sites in a wider defensive networks, with the open field sites serving as muster grounds for the fyrd garrison. Rather than flee to the burh, local populations would flee to a local stronghold - such as a repurposed hillfort or fortified settlement - while the fyrd garrison acted as a response force to march in response to any projected threat.
Some sources:
Strickland, Anglo-Norman Warfare
Davies, Domination and Conquest
Britnell and Hatcher, Problems and Progress in Medieval England
Stenton, Anglo-Saxon England
Reynolds et al, Landscapes of Defence
Baker, Brookes and Reynolds, Beyond the Burghal Hidage