I used to think that it was really, really important to know what characters looked like. So important that I wanted to make sure that I described each one as soon as he or she appeared. I would draw pictures of each of my characters so I could understand what I wanted to describe.
Now that I've been writing for a while, I realize the answer to this question is less clear-cut. It has nuances.
Before I hit nuances, though, I will say this: it is not necessary to describe your main character on the first page. Sometimes you can get through an entire short story with only a very minimal sense of what the character looks like. So back away from the mirror scenes, folks, before you make your readers scream, "cliché!"
Right, then. When is it important to know what a character looks like? Here are some factors to consider:
1. In which genre are you writing?
If you are writing romance, the appearance of the main characters particularly is very, very important. Typically, so is the type of clothing they wear. You will also find the trend toward describing clothing and appearance in gothic and steampunk contexts, and sometimes in alternate history. In other genres, whether or not you describe appearance will depend on other factors. Which leads me to...
2. How much of the character's appearance can be supported using existing reader expectations?
If you are writing in mainstream genres or in genres (like historical) that access existing sets of technology, fashion, etc. then you can take advantage of that existing knowledge in your reader and evoke more than you describe. If you are working in science fiction, fantasy or steampunk where the presence of one thing doesn't necessarily imply the presence of another, you may need to put effort into describing more detail in order to defeat incorrect assumptions.
The next set of questions has to do with the nature of the characters in question.
3. Is this an omnisciently observed character, a point of view character or a secondary character?
This is probably the single most important question to answer. If you're using an omniscient narrator, the narrator is the one deciding what visual details of the main character and secondary characters readers need to see. If you're using limited point of view, then what details of secondary characters get described will depend on the mental states, perceptiveness and judgment of the point of view character. And what details of the point of view character get described will depend on how aware that character is of his/her own appearance.
4. If this person is a secondary character, will he/she appear in the story more than once and need to be recognizable?
A character who will need to be recognized later needs to have some characteristic that stands out and is noticed by the point of view character. This feature does not have to be visual, but it often is, and it must be included in the initial description. For example, you might have a character who will be "a guard with a crooked nose" the first time and "the guard with the crooked nose" thereafter.
5. If this person is a point of view character, what aspects of his/her personality lend themselves to a concern with appearance?
The only time you really want a person looking in a mirror is when that person has a habit of looking in mirrors to check his/her appearance. The reasons for checking the appearance will affect how the appearance is described, and they need not occur on the first page where a character appears, but should appear at the point where the concern with appearance is most relevant. A lady might be concerned about whether she looks right for a party and check her makeup in a mirror before walking in, or she might just touch her cheek with one finger unconsciously. I have a character who has to check his appearance constantly so that his boss won't freak out. His self-descriptions are quite detailed but have nothing to do with vanity or the public's opinion.
6. If this person is a point of view character, are there any aspects of his/her appearance which will affect his/her perceptions, judgments, or actions?
When you are using a limited - particularly a deep internal - point of view, and particularly if you're working with a character who doesn't really care about his/her appearance, then this is the question you should be asking. I have a character with very short legs who is taller than the people he's speaking to when he is sitting down, but shorter when he stands up - so I need to be clear about whether he's looking up or down at people at different points. My character Rulii from "Cold Words" is a member of the downy-furred race of the Aurrel, which is enormously important in the story, but not because it's a matter of how he looks. It affects his behavior, his fear of cold, his fear of shame, and his desire for justice (because his race is downtrodden). Those aspects of appearance which affect the way a character perceives things, judges things, or behaves, must be included - but the best way to include them is by demonstrating the effect they have on the character rather than stepping outside the character to observe them.
7. Are there any questions of appearance that readers are likely to get wrong?
This is a funny one. A character in one of my unpublished novels is very pale and has blond hair, but when my writing group first read it, many of them picked him as having dark hair because a) he is a mysterious character and b) I didn't make explicit mention of his hair color early enough. This is one that you might be able to take care of just by including the basics of eye and hair color that Western readers will be looking for, or it may be something that comes up in critique.
Finally, this seems like the perfect place to address Garrett Anderson's recent question:
"What sorts of strategies would you recommend in describing a character to an audience when the adjectives would not exist in your fictitious world? For example, if I have a character whom I want to look Asian, but there is no such place in my fictitious universe, what are some strategies to convey the appearance? Maybe that's not the best example, but basically, if you want a certain look, and you don't want to use real-world references."
I recommend a few steps. First, ask yourself if this particular appearance is absolutely necessary to your portrayal of the character. If it isn't, don't worry about it - just give a few basic characteristics like maybe dark hair and leave the rest up to your reader. If it is, keep reading.
First, create a sense in your mind of what the character looks like physically. Ask yourself what aspects of that appearance would be noticeable to a resident of your world. Those are the ones you will want to include in your description.
Second, and very importantly, think about why it is that residents of your world would notice these physical characteristics of your character. What is it about that person that stands out relative to all the people around? Does he or she resemble a person of a particular nationality local to the world in question? Does the character's appearance give observers a "vibe" like the one that an Asian appearance would give you? Where does that vibe come from? What associations are people going to make with that appearance when they see it? Those associations have to be grounded in the world you have created.
I actually have a character whom I imagine as vaguely Asian-looking. I don't describe him at all until the third page of his opening chapter. You'll notice (and laugh at me no doubt) because this is a mirror moment (not a whole scene, thank goodness). This description comes at the point when he's just finished showering and dressing before a job interview, and gotten into his black silk suit:
"He plucked up his favorite tailed comb and trained his dark hair into its ponytail, which thanks to Kiit's precise trimming, fell just outside his collar. At the mirror he shared with his bunkmate, he painted the small black circle between his eyebrows, cleaned his makeup brush and shut it into the box of implements atop his dresser."
Most of his "vibe" comes from his attitudes and his actions rather than his appearance. If readers don't see him the way I do, that's fine with me.
I hope this helps you all deal with the question of appearances!