"Monster hunting" Burntcustard does not go 'hunting' - that would imply failure. Burntcustard goes killing."
- Burntcustard talking in 3rd person

*Update!* - As of the beta 1.2 update, stone and iron weapons and tools last twice as long! I will update this post when I upgrade my computer and can take a better quality video.

Part 1 of this guide covers strategies and items used to kill Aggressive mobs whilst up close. (Not including creatures from the Nether)Whilst playing Survival Single Player on Normal difficulty.

The basics
Monsters in Minecraft can be a nuisance, a tool for getting loot, or can be killed for fun*

*Killing for fun is not a good enough reason to kill any of your pets, siblings or associates in the real world.
Monsters all have 10hp (hit points) each, and objects which are not weapons or tools only do 0.5 damage. It is not a good idea to take on monsters, or even go outside during the night with only your fists as defense. Swords allow you to dispatch monsters quickly, and are nearly essential for survival.

Detailed Comparison  
This video and table shows attributes of the most commonly used close combat weapons in Minecraft. Other tools are not included because they do not kill monsters efficiently. Look at the table here if you want information about other tools. The "Stone/Iron Sword" values are for 4 stone and 1 iron sword.

Wooden Sword
I do not recommend the wooden sword for killing Monsters, whatsoever. A...