From the Anniversary Update
Woodcutting Axe & Pickaxe - Your first two 'weapons' are meant to be used against wood and stone, not flesh, so don't expect easy kills. But they're useful enough for scaring off small attackers like wild pigs and crocodiles.
Nightstick - Cheap as dirt and easy to craft - just find a stick! This simple weapon is more effective against the living than a woodcutting axe or pickaxe and it never degrades. It also appears in the crafting blueprint for nearly every other weapon. Plus you can light it on fire in a pinch!
Stone Hammer & Metal Hammer - If you can find (or mine) a small stone, simply add it to your nightstick and *bam* - insta-hammer. With this weapon you can defend yourself against most creatures, though you'll have to replace it often. A metal hammer is made with iron ingots - it's rarer and much more expensive, but far more durable.
Trainer Bow & Composite Bow - These weapons are difficult to craft and use, but worth it if you don't like close combat. A trainer bow doesn't have much range or power, but it's easier to use without the Bow skill. The composite bow has range and power to spare but without the Bow skill you're as likely to hit yourself as the target.
One Handed Axe & Two Handed Axe - These axes are expensive and they're useless against plantlife but they make short work of wildlife. The one handed axe is smaller and will fit in your average sack. The two-handed axe is more powerful, but it also requires a backpack, and you can't carry a lantern while using it. If you plan to fight a bear in close quarters a two-handed axe is the only weapon for the job. Like all axes, they take a long time to swing.
Shortsword & Bastard Sword - These are good all-around weapons. They're durable, they swing relatively quickly and they're effective against plantlife and wildlife alike. The Shortsword is less powerful but requires less iron.
Rapier - All the damage of a Shortsword with half the swing time. This sword is expensive to craft but durable and useful when dealing with a fast creature.
??? & ??? - These strange and exotic weapons are spoilery so you'll have to wait for the final game to see them...
Language is to the mind more than light is to the eye.