This varies immensly with time and place.

There were castles in Sweden that were the residence of the appointed tax collector, which usually was a nobleman (and sometimes a mercenary captain rewarded by the King with the position) - these type castles would see many different residents and garrisons over the years, and were frequently destroyed in uprisings.

Other castles were very lightly (or not at all) garrisoned and intended to be used in times of trouble. The royal castles built in Wales by King Edward of England usually had a minimal garrison. Conwy's, for example had a constable (commanding the garrison), 30 soldiers, 4 artisans and a chaplain. The Scottish clan castles were often of this type.

Other castles were the holdings of a specific family and were manors as well - they had land, cattle, business, serfs (or tenants) and perhaps even industry attached to them, and a caretaker or the owner himself in residence.

So yes, many of the more powerful and influential people of the era, nobility who owned a lot of land, lived in castles or fortified manor houses that were castle-like. However, not all castles were manors or even especially suitable for long-time residence but rather built as a short-time refuge in times of trouble.

In order to answer your question, we must divide castles into several groups:

1. Refugial gorod. This type of "castle" or more likely a wooden fort was occupied only during times of trouble, essentially only when the local populace was attacked. This type was very popular in the Iron Age, and early medieval times. Usually almost nobody (save for the guards, maintanence and fee collectors) would permamently live there.

http://images40.fotosik.pl/1704/8487b5248c31c55c.jpg

2. Keep. Similar to the one above. This would be a small, stout and tightly packed castle or fort, intended to "keep" valuables, stock of grain, and people away from danger of being raided, pillaged or stolen. This type was very popular in Early Medieval times. This type was infamously unpleasant to live in: cold, windy, dark and dank, and vast majority of nobles responsible for governing such a keep would rather live in a manor somewhere else, and only visit it in times of need. The false impression laid by the media, that people lived often in such castles comes from the fact that due to their stout structure, lots of those survived, and thus seem very popular.

http://mw2.google.com/mw-panoramio/photos/medium/80556511.jpg

3. Stronghold. This type was larger than a keep. Strongholds were built on important spots (intersections of trade routes, rivermouths, throat of a valley, dry route through a swamp etc) to garrison men, hold against an invasion on internal uprising, and most importantly, to collect tolls, fees, and taxes from the local populace and merchants. The main difference (other than size) between a keep and a stronghold, was that a keep would be often of only local importance, while a strongold would very important, profitable (taxes and tolls) funded by the crown, well garrisoned, and people would live in it. It would be the home for not just the lord (castellan, holder of the castle) but also for various tax collectors, artisans, clerks, trainers and sergants, minor clergy, etc. Strongolds remained popular, in a form of military fortification, almost up to WW1.

http://www.kogis.pl/gallery/medium/ph744tofertar6786.jpg

4. Knightly tower/familial turm (stand-alone motte). This was essentially a tiny keep, in a form of a single 2-4 stories high stout tower, intended as a home and a keep for a single knight, his family and retainers. Most of those would be more or less the same size as small modern water tower, and surrounded with a pallisade. Within the pallisade, would be also a space for various sheds, cottages, workshops and a separate kitchen (kitchens could not be built into the tower itself, since it usually had no chimney tunneling). Many knights and lesser nobles would live in such a tiny "castle", and such an arrangement remained popular until the early 17th century, when towers become "unfashionable", and lesser nobility started prefering to live in mansions/manors.

http://upload.wikimedia.org/wikipedia/commons/c/ce/Ireland_tower_house_near_quin_county_clare.jpg

5. Nestled castles/highcastles. This type of a castle exists within a city, usually on hill or series of hills. Sometimes it was a case of a city growing around a castle (this is evident in cities where the castle is right in the middle, and surrounded with wider and wider encirclements of walls and the arrangement of "higher" and "lower" city, that was closer or further away from the castle proper). Other times, the castle would be built close to an important city, usually in a highly defensible position (on a steep hill, by a cliff, in the fork of a river etc) and the city would grow out to encompass the castle.

Such castles were always lived in, and were designed to be so. The internal arrangements of such a castle would combine the qualities of a large mansion, a government building and a set of internal workshops, kitchens, cellars, storages, dungeons etc. These castles would often be joined archtecturally with a church or a cathedral, often with a roofed passage.

This "pallace-castles" were always lived in, and it was quite a prestige to be awarded one. Not all of those belonged to the monarch and were held by a nobleman; for example, one of the biggest castle-complexes in all history, the Marienburg/Malbork castle, which perfectly fits this description was a home to the Teutonic Order of monk-knights.

http://www.pomorskie.eu/res/kultura/zamki/malbork1_450.jpg

To sum up: Castles were occupied when it was profitable or prestigious to do so. The main problem with living in a castle, is that it was usually far less comfortable than living in a mansion, and that it was usually positioned away from where everyday life happened. Castles were built on hills or next to cliffs, on small islands, and in the forks of a river, while most cities, villages and manors were built on a plain, next to an easily accesible riverbank. This meant that unless the distance between the castle and the town/village was small, it would be a nuissance to dwell in a castle, and rural manors were prefered instead.

Another note: for the first several centuries of the medieval era, monarchs would rarely live in one place (castle or otherwise) but rether travel along the path linking the castles and manors of their retainers, to gevern things directly (so called rex ambulans). Historical sources claim that the arrvial of the monarch and his court was a great prestige for the local lord, but also that housing such a guest was incredibly expensive, often enough to bankrupt minor lords.

Sources:

Thompson, M. W.,- The Rise of the Castle

Guerquin B. - Castles of Poland

Kajzer L.- Lexicon of castles

Kajzer L.- Castles and society