In Minecraft, Mobs are everywhere, especially when they include monsters. This part of the Guide has two sections, Mobs and Animals. Both are important, even Animals, as animals are a main food source.
Animals: Animals in Minecraft are extremely important, as they are usually your first food source. The aren't aggresive like Monsters, and all of them, with the exception of Pigs, also drop other goodies. Cows drop Leather, useful in Armor crafting and books. Chickens drop feathers, used for Books+Quills and Arrows. And finally, sheep drop Wool, useful for all sorts of things!
Monsters: Monsters in Minecraft are optional. You can get four different levels of intensity for these Mobs. Peaceful, which as you can probably tell, has no monsters, Easy, Medium and Hard. I would recommend that when starting out you leave out monsters and stay on Peaceful. But if you really, really want to fight these beasties, I don't think you should go any further than easy (unless you're a Daredevil) and build up your defenses and get better weapons. You can go to Minecraft Monsters-Minecraftopia to learn how to defeat these evil-doers.