Some ideas:
Elves: Elven Bow
Elves are famous for their skill in using bows, so they could have a stronger bow, that can only be used by them.
Dwarves: Dwarven Axe
With their colossal strength and their unbelievable ability in forging powerful weapons, dwarves might have invented a light, but strong axe, that is fast (because it's light), but still can inflict tremendous damage.
Halflings: Slingshot
Halflings are famous for their dexterity, so they might use a slingshot with stones. The advantage of this weapon could be, that it has infinite ammo. Small stones can be found almost everywhere and they are very light. So, you can say, that you can always have some in your pocket or in a small bag. As disadvantages, they do much less damage than a bow or a crossbow.
Lizard: Tridents
Lizards are creatures of the water and tridents are connected with the water since the old Roman and Greek Empires, because of Poseidon and Neptun.
These tridents are long range weapons, which inflict much damage.
Orcs: Giant Bats
Although orcs aren't very large, they are extremely strong and have a good stamina. So, they could fight with this very blunt and crude weapon, that might be very slow but deadly.
Last but not least:
Humans: Dual Swords
Humans aren't very well known for using a special weapon, besides the sword maybe.
With their mixture of strength, dexterity and speed, the usage of two swords is destined for humans. These swords can be used to attack quite fast, but also to have a strong defense. With two swords, you can block enemy weapons very well. (except distance weapons)
These weapon could be carried by other races, too, but never used.
I have no idea, how difficult it is, to limit items on a certain race, but I assume, that it isn't that hard.
These suggestions are only some ideas. If someone has better ideas or wants to give comments on the current ones, please do so.
Rovac gave me some ideas, too. Thanks!
EDIT:
Additional idea: I think, the different weapons should only be crafted by the matching race and a master of the profession.
Elven Bow ---> Elven carpentry master
Dwarven Axe ---> Dwarven blacksmithing master
Slingshot ---> Halfling tailor
and so on...
I would be illogical, if Elven blacksmiths, for example, knew how to create a Dwarven masterpiece of craftmenship.
(Edited by Sharag at 3:05 pm on April 7, 2002)