It seems self-evident that the phenomena we sense are accurate and correlate to the real world.
What sorts of philosophical arguments might cast doubt on this conviction in the veridicality of perception?
"Distrust your senses" is a very long tradition. Recall Plato's "cave" analogy from the early dawn of philosophy, ~400 BC.
Plato postulated that there is a reality outside of what humans experience. He compared the human "experience through the senses" to the experience of a caveman looking at a shadow play on the cave wall: The caveman can only see the shadows on the wall, he/she has never experienced anything else, and believes that those shadows are all that there is of reality.
Plato says that there's a reality outside of that: For the caveman, there's someone or something outside the cave that's projecting those shadows. There's a sun (or something) that provides the light, there's a whole world out there, but the caveman looking at flickering shadows on the wall may not even realize that the outside world exists. The caveman's senses (and of course, by analogy, any human's senses) can only tell that "this thing here is a shadow" and "that thing over there isn't". Plato's argument is that it doesn't matter how accurately our senses can detect shadows on the wall: The argument is that there is a reality outside of what our senses can perceive.
It's not hard to make modern analogies:
Suppose someone were brought up from birth exclusively on Hollywood movies, and had never seen the outside world. Would that someone be aware of the existence of scripts, cameramen, film sets, directors, actors, people whose only job is to do makeup or lighting? Or would they assume that whatever Hollywood showed them was reality?
Suppose that I'm watching a movie, and my senses tell me that this guy that they call the Joker is a very bad guy, while this other guy called the Batman is a nice guy and is going to save us all. What exactly does that sensory input (and my interpretations of it) tell me about reality?
Suppose that we all live in the Matrix, and that all our sensory inputs are created by somebody else, for some unfathomable (to us) purpose. Is there any way that an "I" living inside the Matrix could tell that my sensory experiences differ from an "I" living outside the Matrix?
That's the basic argument of Descartes: How can my senses tell me whether I even exist, given that there might be a god somewhere dreaming the entire world, and we're all living inside the god's dream?
Descartes famously answered "I think, therefore I am": If I have more or less control over my own thoughts, nothing else matters, and I have an existence independent of whether it's inside a dream. (I'm not arguing whether this is a good or bad argument, I'm just saying that historical philosophers have struggled with these questions. I can point out that Neo in The Matrix might very well ask himself the same. The external agent has changed, from God to hostile AI, but the question remains the same.)
Suppose that you people live in the real world, but I personally happen to have a very fond relationship to drugs and magic mushrooms, and every bit of my senses are telling me that there's an extremely lifelike dragon attacking me right now. Should I trust my senses?
There are lots of reasons to distrust our senses in general, even primary sense experiences like color and lightness. Illusionists, optical illusions, and drugs, show that even immediate senses can be fooled. Physics shows that there's a lot of the world that humans were hardly even aware of: Ultraviolet, X-rays, radio waves, radioactivity; none of which is directly perceptible by humans, but it's still real. So our direct sensory impressions can't be trusted too far either. That's perhaps a more modern argument, and these days it's not hard to find examples where our immediate sensory impressions are simply wrong.
Kant says that there's the "world as it is", which humans can never actually know, and there's the "world as it appears to me". We try the best we can to extrapolate our "here and now" limited sensory experience to rules applying to the world in general, but we'll never be able to know the "real" reality, we'll only know the simplified model we've built up inside our head based on our limited experience. And there is no amount of experience that will let us know everything.
The original philosophy argument, from Plato 2500 years ago, didn't doubt sense impressions as such: The cave analogy assumes that the sense impressions of the caveman accurately reflected the shadow play on the cave wall. The philosophical objection is that there might be an entire world outside of what humans happen to perceive, for some reason that the observer simply doesn't know about.
The basic response to this question (whether you listen to ancient philosophy, early/late modern philosophy, or pretty much anybody who's thought much about it) is that "you could always be missing something".
Carneades: It's basically impossible to KNOW anything with certainty, because you can never know how much you don't know. But you have to live life, so just go with what seems the most reasonable to you.
Descartes: No matter how accurate and valid your experiences seem to you, it doesn't guarantee that you're not getting something horribly wrong / being tricked / living in The Matrix, etc. That's okay, I have a special argument about the existence of God that can solve this problem...
Hume: Just because you woke up today doesn't mean you'll wake up tomorrow. In fact, it's impossible to even give a PROBABILITY that you'll wake up tomorrow - because the past says nothing about the future.
Kant: We actually can't know much of ANYTHING about true reality (things as they are) - but only subjective reality (things as we see them). That's okay, because I have a special system on which to build a theory of the human mind, truly universal ethics, and even arguments about the existence of God...
... and so on and so forth.
They don't; that is not all do; for example the natural philosophers; most, of whom are now called scientists, and in antiquity physilogoi took their sense on trust; if you are going to physics as Galileo or even as Einstein did - you'd better be able to trust your measurements.
It was Descarte that popularised the view that one shouldn't trust one sense; but this is a travesty of his views; he was looking for a secure point from where to begin his theory of true and justified knowledge.
There are broadly two issues.
The first is that our senses are accurate in some respects and correlated with the world in those respects. But our senses also have flaws as illustrated by optical illusions. In addition there is a lot of stuff that we don't sense except in an indirect way, e.g. - neutrinos and some kinds of electromagnetic radiation. So sense information has to be interpreted carefully to learn about how the world works. Nobody who understands how their senses work would trust them in the sense of uncritically assuming they are correct.
The second issue is that many philosophers hold a theory according to which knowledge is justified true belief. Justification is an alleged process that shows that a particular idea is true or more probable than its competitors. In reality, you can't prove any position or show it is probable. Any argument requires premises and rules of inference and it doesn't prove (or make probable) those premises or rules of inference. If you're going to say they're self evident then you are acting in a dogmatic manner that will prevent you from spotting some mistakes. If you don't say they are self evident then you would have to prove those premises and rules of inference by another argument that would bring up a similar problem with respect to its premises and rules of inference. Sense information isn't derived from anything and so it is not justifiable As a result justificationists (those who believe in justification) who take their ideas seriously have to reject sense information as unjustified.
In reality all knowledge is created by conjecture and criticism. You notice a problem with your current ideas, propose solutions, criticise the solutions until only one is left and then find a new problem. Experiments are useful only as criticism. Ideas can't be derived from experiment any more than from any other set of premises. Rather, the idea is that you work out how the consequences of one theory differ from those of another. Sense information can play a part in criticising proposals. If you sense something that is apparently incompatible with some theory you hold then you must add to your knowledge to account for that. You might scrap your old theory and come up with a new one, or you might find that your initial interpretation of what you sensed was wrong. Also, in general it's a bad idea to describe stuff in terms of what you sensed. It is better to say that some particular event apparently happened and then to draw conclusions about what a person would sense if there is a particular reason to do that. Saying that the event happened provides you with more ways to test whether you sensed what was going on correctly because the event will have implications other than what you happened to sense.
For more on this issue you might want to read "The Beginning of Infinity" by David Deutsch, Chapter 10.
The previous answers here already covered the theory pretty well, but here are a few practical examples to further the point that you cannot rely on your perceptions of reality as being reality itself.
Inattentional blindess: also called perceptual blind, this is where your senses experience something, but you do not have at that moment the capacity to process the information because it is unexpected in the context of the observation. This failure of perception is always a potential and can cast doubt on whether a sense is truly perceiving the whole picture. The example that comes to mind first is The Invisible Gorilla (Christopher Chabris and Daniel Simons), but wikipedia has many more examples.
Color test: a page of colored words are placed in front of you and you are asked to read the words (or say the color of each word). The words are all names of colors, but the color of the word does not match the description of the word. Your brain will eventually start confusing the two perceptions.
Another common example is the placebo effect which has been in use in medicine for hundreds of years and has ancient roots.
So, you said, "It seems self-evident that the phenomena we sense are accurate and correlate to the real world," but I would argue that with these examples it is plain that our senses are highly contextual and subjective.
You may wish to read the visible and invisible [hereon VI] by Merleau-Ponty, which covers questions like this. Though he never edited it into a complete or particular clear work.
He has always talked about perceptual illusion quite a bit. Philosophers [and myself] don't "trust" their senses because there is reason to believe they can be wrong.
To take a step back, this itself could be seen as philosophers being rational or seeking rational answers. Or, it could be seen as trying to squeeze insight out of quibbles. I actually see VI as quite a populist [yet continental!] philosophy: he is trying to bring philosophy to the masses by way of a semi mystical experience.
Of course taking philosophy seriously is not quite the same as being a philosopher [i.e. producing philosophy].
"Until the 20th century, reality was everything humans could touch, smell, see, and hear. Since the initial publication of the chart of the electromagnetic spectrum, humans have learned that what they can touch, smell, see, and hear.. is less than one millionth of reality" - Buckminster Fuller
Although we should not "blindly" trust our senses, likewise we should not "totally" distrust them.
Just because we cannot "sense all of reality," it does not mean that our senses cannot be trusted for the part of reality they can sense.
Also, since we have had, and continue to have, communication with each other, our collective "sensing" ability has allowed us to "sense" (become aware) that reality is much larger than the reality revealed by our individual senses. Our grasp of the "whole reality" will increase as our individual senses are augmented by our technology and our greater number.
Our senses are not evolved for accuracy. Our brains make an attempt to fill in the blanks whenever our senses fail to recognize something. From an evolutionary standpoint this is advantageous.
Consider a caveman in a wooded area who sees a predator in his peripheral vision and runs away. He may have actually seen a simple rustling of leaves in the breeze and his brain filled in the blanks with more important information. Either way he lives to pass on his DNA.
Consider another caveman is encountered with the same situation and his brain DOES NOT fill in the blanks. Sometimes this one lives, sometimes he dies.
This is a well documented phenomenon and similar things happen with auditory phenomenon as well.
Moreover, as time goes by and we attempt to recall past events our brains try to fill in the blanks again with new things that we might have learned since the original event happened.
Therefore our own senses are vulnerable to our interpretations of them even without our own knowledge of any possible changes.
The famous story of "Blind men and an elephant" perfectly describes why we cannot trust our perceptions. You can find the story at http://en.wikipedia.org/wiki/Blind_men_and_an_elephant