This is a post that I have been meaning to write for a while, but I have had a hard time coming up with a good thesis for it. So instead, I'm just going to give a few examples of what I think qualifies as a monster.
These are creatures that should not be. Their very existence goes against the natural order of the world. They are twisted mockeries of life. They are formed not by nature but by sorcery, science or both in some cases. Abominations usually come in two varieties; corruptions of an existing lifeform or an attempt to create a new form of life. The former includes the undead and, depending on the campaign setting, orcs and mutants. The latter includes fusion creatures like the owlbear and created life like the golem or robot. Whether or not creatures like these can be redeemed usually depends on the nature of their creation. Accidental creations may not be inherently evil. If the corrupted subject was good in his previous life, that goodness may still exist in his new form. Likewise, beings that are created may not turn against society if they are accepted by at least a few decent people right away. But often, the process that creates the abomination drives it mad, and makes it a danger to all around it.
This does not refer to the rubber-forehead variety seen in science-fiction. Rather, this is more about a lifeform whose existence is so radically different from humanity that there is no way for a normal person to relate to it on any given level. These beings may look at humanity as we would look at an unintelligent animal, if we're lucky. This means that the characters are faced with something that is a threat simply because it does not recognize what we are as sentient. We are food/raw materials/pets/whatever to this being, and it will accept no alternative. Especially not equal.
Society has it's share of dangers. These usually are in the form of creatures, or groups of people, that choose to take what it wants from civilization through force. While the dragon that demands a virgin sacrifice or the wyvern that steals the local livestock are the usual staples of this type, ever-present threats include more 'mundane' dangers such as bandits and pirates. The latter groups usually have outlaw status, meaning that they suffer from no protection under the law. This makes it legal for any person to kill, steal or enslave them. In many medieval societies, outlaw status was an effective death sentence. This tends to create a certain mindset in some people. After all, if your rights to life, liberty and property were stripped from you, you too may become a dangerous person, if only out of self-preservation.
Just Plain Evil
A lot of people don't like this category. The idea of someone or something just being evil is one that most people have a problem with. Surely there has to be some extenuating circumstances that has made the villain what he is? While it is true that for some people life sucks, it is also true that some people just don't give a rat's ass about others. Sure they may pull out the 'bad childhood' card every once in a while, but it is usually in order to dupe some naive do-gooder into helping them with their nefarious tasks. These people are self-centered assholes that will do whatever it takes to get what they want. Some are overgrown bullies that are in desperate need of an ass-kicking, others are master manipulators that manage to convince other to do their dirty work for them. The worst part of these types is that some of them don't even see themselves as being evil. Instead, they believe that they are performing a 'greater good' with the death and destruction they sow. The ones that know they are evil tend to be a bit more sadistic as they play with the lives of others. This type of monster is as likely to be a normal human as they are a fanged creature from the netherworld. A fact that makes this category one of the scariest.
By no means is this a definitive list of monster types. There usually is some overlap between categories. As I mentioned in the beginning, I had a hard time coming up with this post, hence the unfocused nature of it. I'm sure others may be able to come up with other categories, or better examples for each category. So it begs the question, what do you think?