What weapon does the most damage in early game?

I just started playing Minecraft today and was unfortunately eaten alive by a horde of angry looking block spiders. What weapon does the most damage at the beginning game?

Minecraft Wiki has a table of damage done by weapons.

Swords: The best ordinary weapon (by damage numbers) you can readily make is an iron sword, and the second-best is a stone sword, which is very easy to craft since it only requires wood and cobblestone.

Bow and arrows: I strongly recommend keeping a bow and arrows, if you can, because it enables you to kill monsters at a far distance (especially important since spiders jump at you and creepers will explode without actually touching you). A bow requires three string and three sticks, so the hard part is killing enough spiders to get the string. You could:

• Kill spiders in the morning, when they will only attack you after you attack them and so won't swarm.
• Build a trap for wandering spiders; for example, a wall of cactus which you're on the other side of. However, this isn't as easy now that spiders can climb; you'll have to put an overhang on top so that they climb up it and stop.
• Or just kill spiders with your stone or iron sword.

Arrows for a bow are made from flint, feathers, and sticks, or are dropped by skeletons. Flint is readily obtained by mining gravel (any gravel that doesn't produce flint can be re-placed and mined again for another chance at flint), and feathers may be obtained easily from chickens.

Burning: It is possible to set enemies on fire, but it doesn't kill them very fast. A more practical possibility is to drop a bucket of lava. The safety of this depends strongly on the terrain (you can outrun lava unless you're clumsy, but the real hazard is if the flow blocks you from walking back to pick up the source), but if you can do it then it will bog down the enemies that try to chase you across the lava and kill them reasonably quickly.

Armor: Also, find a herd of cows and start breeding and slaughtering them to make leather armor (24 leather makes a full set). Armor makes you take a lot less damage, if nothing else so you can get in some aiming and timing practice in those beginning fights. Also, killing cows and chickens will help you learn how far your weapons reach and how to aim at a mob.

On the Keeping of Cows and Chickens: Passive (non-hostile) animals spawn rarely, mostly on initial world creation. Therefore, in order to obtain the leather and feathers I recommend above, you will need to breed them. A complete discussion on breeding would be a bit much, so I'll just point you at Minecraft Wiki on the subject. The short version is that you should construct a wheat farm (as wheat is required to initiate breeding) and a pen for the animals. If you do not breed animals but only kill them where you find them, you will be waiting a long time for the population to recover. Also, baby animals do not drop any items, so you must wait for them to mature.

The current answers aren't quite up-to date, so here's the current info, as of Minecraft 1.0.0. While not all of these are obtainable from the beginning of the game, it's all useful information. All data is pulled from Minecraft Wiki or my own personal experience.

Base Stats

Swords: The most easily obtainable weapon also deals the most raw damage. Wooden swords are the baseline, dealing 2 hearts of damage. Stone, iron, and diamond each increase the damage amount by half a heart, capping out at 3.5 hearts with a diamond sword. Swords are easy to make and use, but have the downside of no range.

Bows and arrows: Both bows and arrows are more difficult to craft than swords, and are not obtainable right when the game starts. Also, arrows need to be replenished, so there is a higher amount of maintenance when using a bow. However, they are much safer than swords since they give range, especially when fighting Creepers. Arrows do not, however, do as much damage as swords, with just a half a heart of damage per arrow.

Flint and steel (fire): Fire is a possible method of combat, though not recommended. With flint and steel, you can set blocks on fire, lighting any mobs that walk into it up. The fire itself will deal a heart of damage per second. Even once they leave the flames, they will continue to take damage at a half a heart per second, though the fire will eventually go out if left too long or if the mob runs into water.

Lava: A bucket full of lava is arguably the most powerful weapon in the game. It will deal 5 hearts of damage per second while any mobs are inside. It will also light them on fire, doing the fire rate of half a heart of damage per second. Also, it can be easy to obtain with just three iron and a cave or surface lava pool, and it has infinite durability. Of course, it has its downsides. The most obvious is that it's extremely dangerous since it's deadly to the player as well as mobs. Another downside is that all dropped items from the killed mobs will be obliterated.

Critical Damage

Swords: Criticals with melee weapons are easy to obtain, and will consistently increase your damage with no downsides. Criticals with wooden/gold swords deal 4 hearts of damage, and each tier increases that value by 1.5 hearts. That means a critical with a diamond sword deals a whopping 8.5 hearts of damage, enough to kill nearly all enemies in the game with one or two hits.

Bows and arrows: Though the base half a heart damage value may seem like a tiny amount, charging your bow shot can vastly improve that stat. Holding the fire button will "charge" the bow, and a fully charged bow shot can do up to 4.5 hearts of damage. That's much more effective than standard bow shots, and makes the bow a seriously powerful weapon in combat.

Enchantments

Swords can be enchanted to deal additional damage.

Sharpness: The most basic enchantment, it deals an additional 1.5 hearts of damage per level. Sharpness can go to level V, so you can get a bonus of 7.5 damage on a sword.

Smite: This enchantment, also capping at level V, deals an additional 2 hearts of damage per level. However, it only deals the additional damage on zombies, skeletons, and zombie pigmen.

Bane of Arthropods: Works exactly the same as Smite, but works upon spiders, cave spiders, and silverfish.

Fire Aspect: Does not directly increase damage, but lights all mobs you hit on fire, dealing half a heart of damage per second. While this is extremely helpful, it's useless against Nether mobs, since they are immune to fire.

Knockback: While it technically does not inflict damage, it causes mobs to be flung back, making dealing with them easier. It only goes to leve II, which increases knockback distance.

Looting: This helps with combat, yet also does not directly affect your damage dealt. Extremely Rare enchantment. This enchantment causes all enemies to drop the max amount of all items they drop when they die, rare and common. eg. Cow drops 4 leather and 6 meat.

Potions

Potion of Harming: Quite simply does damage to the drinker. Brewing it as a splash potion will allow it to be used as a sort of grenade against enemies. It deals three hearts of damager per level at the splash's center, up to level II. A major downside, though, it that it will heal undead enemies, zombies, skeletons, and zombie pigmen.

Potion of Healing: Works exactly the same as the Harming variety, except it heals three hearts per level. However, it can be used to deal damage against undead mobs.

Potion of Poison: Deals slow damage over time to enemies in the blast radius. Note that it does not effect spiders, cave spiders, or zombies.

Potion of Strength: Increases melee damage by 1.5 hearts per level, up to level II. The base potion lasts 3 minutes, but can be extended with redstone to 8 minutes. The II variety only lasts 1:30, so while it's effective for quick bursts of damage, for the most part, the 8:00 version is more effective.

Potion of Fire Resistance: While essentially a defensive potion, it also protects the player from lava damage, making using a lava bucket as a weapon perfectly viable. The base potion lasts 3 minutes, and the extended potion lasts 8, with no downsides. This makes the lava bucket very powerful, since the player no longer has to worry about killing him/herself.

Preventative Measures

Though I will not go into them here, there are many additional methods of preventing damage rather than simply dealing it. These include armor, enchantments, and potions. These are sometimes more effective than just dealing raw damage, since being able to stay alive is still the priority, and however powerful your weapon is, a direct Creeper to the face can still kill you armorless.

Additionally, stay fed. Keeping your hunger up will keep you healing, allowing you to remain in combat for longer. Potions can also increase the health regeneration rate or heal health instantly.

Most items (and using your bare fists) will inflict 1/2 a heart of damage to a mob. There are a handful of items that will do more, however. (taken from the Minecraft Wiki)

• Wooden / Golden Sword: 2 hearts
• Stone Sword: 2.5 hearts
• Iron Sword: 3 hearts
• Diamond Sword: 3.5 hearts
• Arrows: 1/2 - 4.5 hearts (depending on the charge of the bow)
• TNT: 12 hearts

Axes are the next best tool to use in combat, dealing 1/2 a heart less damage than their sword counterparts. Pickaxes do 1/2 a heart less damage than axes, and shovels 1/2 a heart less than pickaxes. In my opinion, in the beginning game, a Stone Sword is the most efficient item. Two Cobblestone and one stick is easy to obtain.