It's pretty much taken as read, after fifty-odd years, that the Doctor fights monsters. This has been the subject of much debate--shouldn't the series have more moral complexity? Is it right to portray aliens as "monsters" and humans/humanoids as heroes as the default setting, even if it is sometimes deliberately subverted (as with the Ood and the Silurians)? But to me, it seems to be worth taking a moment to figure out exactly what we mean by "monster" to begin with. It seems like the basic component of a "monster", as defined in Doctor Who, is "an enemy that cannot be reasoned with". The Doctor frequently tries rational arguments against his opponents; it's just that they very rarely work. (Rarely is not "never", though. Look at 'Forest of the Dead', which basically ends with the Vashta Nerada becoming smart enough to realize they should probably let the Doctor go just on basic survival principles.)
But if it's "lack of reason" that makes a monster into a monster, the question then becomes, "Why can't anything be reasoned with in the Whoniverse?" (The obvious answer, of course, is "Because then the stories would be short and boring.") Still, I do think there's something to be gained by looking at the in-story reasons that monsters are monsters in Doctor Who...so consider what follows a rough taxonomy.
The first category is the non-sapient monster. This is, essentially, the mindless animal that preys on whatever is around it. Your basic Vashta Nerada, your Mandrel, your Kroll, your Taran Beast. It attacks the Doctor and whoever's around because they're around, and because it doesn't know what else to do with something that's in front of it and living. This is frequently subverted through the solving of a mystery of some sort: The Doctor figures out that the monster is protecting its young, the killer turns out to be smarter than expected (and moves into a different category of monster), or the creature gains sapience and learns how not to be an indiscriminate killer.
The second category, closely related to the first, is your inimical intelligence. These are creatures that have intellect as defined by their ability to plan and communicate with their own kind, but it's an intelligence of an order so different from ours that there is no room for co-operation or mutual understanding. The Flood from 'The Waters of Mars' is the perfect example of the inimical intelligence; it can talk, it just doesn't bother because it can't see us as anything other than hosts. It's more dangerous than the first category of monster because it can reason, but it still can't be reasoned with. Arguably, the Daleks and Cybermen could fit here, because they are intelligent but are limited by their programming, but as we'll see, they're a little bit more complex than that.
The third category is the uniform mentality. These are intelligent, and can even understand rational arguments against their position; but for one reason or another, they share a set of goals, ethics and beliefs so closely that all of them respond identically to identical stimulus, and they generally have a belief system that precludes meaningful interaction with those outside the group. This can be because they have been programmed (like the Daleks, who are unable to conceive of pity because of limitations put on their mind by Davros) or because their culture produces strongly-conditioned belief systems (like the Sontarans, who have been raised from birth to glorify military triumphs and who breed for uniformity of thought and body), or simply because they share a group mind (like the Rutans, at least in theory). Fanatics and cultists tend to fall into this category, like the Krillitanes attempting to solve the Skasis Paradigm. (The Cybermen would also fall into this group.)
The fourth category are those I'd term "monsters of circumstance". These monsters would not always be monsters, but in this particular situation, they are forced to act in monstrous ways. The Saturnyne "vampires", for example, have no particular emnity for humankind...but they're on Earth, and allowing us to live would mean the extinction of their species. As such, they cannot be meaningfully reasoned with because their desperation makes alternatives seem impossible. Other examples here would include Scaroth, and even Erato from 'Creature from the Pit'.
And finally we have the worst monsters, monsters of choice. These are sapient entities capable of understanding rational argument and a code of ethics...but they refuse to listen to rational argument about the ethics of their actions, because they don't subscribe to an ethical code and refuse to behave in a moral fashion. The Master, the Slitheen, the Weeping Angels...all of these enemies understand perfectly well that what they're doing is wrong. They just don't care. Either the profit it gains them is greater than their feeble moral sensibilities, or they just like inflicting suffering on others. It's worth pointing out here that a lot of human characters, like Tryst and Salamander and Sabalom Glitz (at least in his first appearance) quality as monsters under this definition...which suggests that maybe the dualism of "monsters and humans" isn't as clear-cut as we like to admit. Doctor Who suggests, in fact, that it's the monster inside that you need to watch out for.