Too much deference!
Short answer is that it varies by period and locale. Long answer...
As with Greek citizens, Roman citizens in the republic and early principate would all have had the right to bear arms, to the best of my knowledge, but no army was allowed in Rome prior to the end of the republic. This was because Roman politics were prone to turning into violent conflict, as with the unfortunate end of the political career of
Gaius Gracchus.
In Graeco-Roman culture one very populous class was expressly forbidden from bearing arms, the slaves. I think as freemen they were entitled to arms, but I am not sure. The aforementioned Gaius Marius (to whom a great many military innovations accrue in a somewhat suspicious manner) caused outrage when, in a rather desperate situation, he decided to arm slaves against Sulla (this may be an exaggeration, I have read elsewhere that it was gladiators he armed, rather than all and sundry).
Which brings up an important point about slaves; sometimes they are armed to serve as bodyguards, or as a military corps, as in medieval Egypt and even Germany. So any generalisation about slaves has to be treated carefully.
Judging from the local way that the military was organised in "dark age" europe, I think it is fair to say that any restrictions on weapons that existed must have been very local. In England and France rulers passed legislation requiring minor landowners to band together to equip one of their number for military service. Greater landowners had to equip more men (the root of feudal service) and even these part timers may have initially had the title
milites (knight or soldier) when so equipped. By the eleventh century a knight seems to have been merely a matter of owning arms and having a horse (chevalier, ritter), though that soon changed, and such men became sergeants and squires.
As Stuart notes, the assize of arms gives us a good indication of the situation in England in the twelfth century. In England in 1100 there were probably about 1,000,000 people and there were definitely about 5,000 knights fees (Domesday Book records attest to this). Half the population would have been women, of course, so you are indeed looking at about 1% of the male population holding knights fees at that stage. An unknown number of mercenaries, money fiefs and household knights would have probably inflated this number to some degree, not counting regular fyrdmen. The 1181 Assize of Arms in England gives us the following information:
Knights Fee or more than 16 Marks in chattels or income = Mail Coat, Helmet, Shield, Lance
Free Men with more than 10 Marks in chattels or income = Mail Shirt, Iron Cap, Lance
Free Men and Burgesses with less than 10 Marks = Padded Coat, Iron Cap, Lance
Robert Bartlett has suggested a frequency of something like 1:9:12 for these armaments, based on what the borough of Dunstable owed to the Royal Levy c. 1200. That works out at something like 100,000 armed men in England (say 20% of the male population).
For serfs things were a bit different. Whilst they were probably were not expressly forbidden from bearing arms, it is doubtful they could afford them or find the means to learn their use, nor were they expected to. In desperate situations, such as the prospective 1101 invasion of Robert of Normandy, a general levy would be called out, and this explicitly included "servants". Apparently, Henry had to instruct and encourage these "country folk" in the use of arms. No special dispensation seems to have been given, so it seems to have been a matter of wealth rather than status [i.e. wealth = status]. A similar situation seems to have been the case for the French before Agincourt.
It is interesting that within forty years of the conquest that the Normans seem to have imposed no real restrictions on English ownership of weapons. I am told that this was not the case in Poland and other formerly pagan areas conquered by the Germans and Teutonic Knights. Restricting the arms of a subjugated people is a widespread practice, and precaution against rebellion.
I have also heard that the crossbow was heavily controlled in England, a close accounting kept on their numbers and ammunition, which was stockpiled in royal castles. I don't think this was a matter of restricting its availability, as much as it was an attempt to buy them all up. There was a papal ban on selling crossbows and crossbow parts to non Christians, which is reminiscent of Charlemagne's prohibition on selling Frankish swords to vikings (and likely other pagans). Keeping state of the art weaponry in the country was wisely deemed important! (and this is no doubt reflected in later governmental control on guns and gunpowder).
The other group that governments are interested in disarming are disbanded soldiers, and for similar reasons as slaves and subjected peoples. Disbanded soldiers were a huge problem, as they would tend to turn to banditry if sent home or become mercenaries, in which case they went looking for a war or someone else to retain them. This last often led to the private army, and could contribute to the overmighty vassal problem. After the Stephen-Matilda civil war in the early twelfth century, one of the first things Henry II did was knock down maybe ninety percent of the castles that had sprung up (timber types, mainly) and royal control on who could build a castle continued throughout the period. Weapons were one thing, fortifications quite another.
With regard to hunting the king's deer, it does indeed refer to those in the king's forest, which is land directly held by the king (not just forest either). Boars and wolves are said to have been protected, and possibly a good deal of other game (but their inclusion might be spurious). Folk who lived in the forest and were not servants of the king might have been prohibited from carrying hunting implements, but that seems unlikely if they were only forbidden to hunt certain animals. The land itself would also have been protected against development or enclosure.
What the king might then do, is sell or rather "rent out" the rights he had restricted to various local landowners and clerics, and collect a direct profit on the lands that way.
Runciman and LeGoff are both worthy reads; if you want to supplement them with more modern scholarship you should also probably look into the works of Robert Bartlett, particularly...
The Making of Europe: Conquest, Colonization and Cultural Change (950 - 1350)
England Under the Norman and Angevin Kings (1075-1225)
Anway, that's enough rambling from me.
[i]It is a joyful thing indeed to hold intimate converse with a man after one’s own heart, chatting without reserve about things of interest or the fleeting topics of the world; but such, alas, are few and far between.[/i]
– Yoshida Kenko (1283-1350), [i]Tsurezure-Gusa[/i] (1340)