~~~~~~~~~~Fighters: any heavy (1d8+), medium (1d6) or light (1d4) missile or melee weapon, or any crossbow.
Clerics: any medium (1d6) or light (1d4) missile or melee weapon, or any crossbow.
Thieves: any medium (1d6) or light (1d4) missile or melee weapon, or any crossbow.
Magic-Users: any light (1d4) missile or melee weapon, or any crossbow.
Here is the unnecessarily lengthy rationale. It all started when I began wrestling with the question of crossbows, and then it snowballed.
Most old-school rule sets I know simply disadvantage the crossbow, with no counterbalancing advantage.* The crossbow takes longer to reload, has roughly the same range, and typically uses the same damage die as its long-/short-bow counterpart. So in game terms the crossbow ends up being one of the worst missile weapons you can choose.
This does not make a lot of sense to me, because historically the crossbow eventually replaced normal bows in most European armies, a fact that would suggest that the crossbow must have some quality to promote it over the normal bow. In game terms, then, the crossbow should have some advantage too.
My understanding is that the crossbow supplanted the longbow in most armies not for its range or its punching power (which are not hugely different from those of the longbow), but because of the ease of use and short learning curve involved training a competent crossbowman.
It took a man several long years to develop the strength, stamina and skill to use a longbow effectively. It took a man about a week to become equally skilled with the crossbow.
So the answer occurred to me to link the crossbow, and longbow, with class weapon restrictions. Only the fighter can use the longbow – no one else could possibly have the combination of strength, stamina, and long years of training. Everyone else gets limited to the short bow or crossbows, and the magic-user can use no type of bow other than the crossbow.
This crossbow house rule then got me thinking about weapon restrictions in general. To be honest, I've often found them a bit artificial. Every cleric in every religion is prohibited from using edged weapons? Magic-Users can use daggers, but they can't pick up a simple club? Or use the same sling that a kid would use to hunt birds? I don't generally have huge issues with "gamey" rules, but these are a bit gamey even for me.
In the past I've tried to solve this by using the rule that says anyone can use any weapon, but with damage limited by class. A magic-user can use a polearm if he wants, but it does 1d4 damage. However, this is also a bit silly. If a magic-user is only going to do 1d4 damage with a poelarm, why on earth would he lug that heavy thing around? He can do the same damage with a dagger without carrying the extra weight.
So I instead rethought weapons in terms of general types, based on the damage they do, and allow different classes to use weapons of particular categories.** The assumption being that the higher-damage weapons require more strength, stamina and/or training than the lighter weapons, in a way similar to the crossbow vs. normal bow principle. So there are heavy (1d8+), medium (1d6) and light (1d4) weapons, as they appear on the weapon's table of whatever rule set I'm using. The division applies to both melee and missile weapons without distinction. With this simple division, plus the fourth category of crossbows (regardless of damage level, since the trade-off is loading time), you get the breakdown at the start of this post, by class and weapon type.
* I'm sure there are some rule sets out there where this isn't the case, but I don't seem to own one.
** This is not the same as class-based damage. With this rule, the magic-user still can't use that heavy polearm, but he can use any simple lightweight (1d4) weapon such as (depending on rule system) a dagger, a dart, a sling, a club, etc. or any crossbow (even if it does 1d6 or 1d8).