Many of you will probably hear this question and think, "No!" Others may hear it and say, "Yes!"
Both sides are right. I'll explain.
The first thing to remember about repeating words is that human beings are wired to be very sensitive to repetition. Ever heard of the rule of 3? We can usually tell whether we've seen something more than once without even thinking about it. The first instance might pass almost without notice, but a second repetition will get our attention, and a third will make us think it's supposed to mean something.
If you're repeating words, people will notice. But it's not inherently good or bad. Everything depends on which words are getting repeated and in what context. I'll look at a few types. Warning: the first few will have you saying, "repeating is bad." Be patient, if you will.
1. Function words. These are little tiny words that don't carry major content. Words like "that" or "which" or "when" or "the" or "in"... or "or"! Since these words are generally given less attention than the others, readers are less likely to notice when they repeat. However, it's good to watch out for them if you find your repetition sensor going off in a particular passage. I often find I've used a preposition more times than I feel comfortable with in description: "the top of the door of the passage" has too many "ofs" for me, and I'd probably go to "the top of the passage door."
2. Verbs. Often in a first draft I'll use a verb like "keep" twice in close succession without noticing. This can also happen in what Janice Hardy calls "revision smudge." You can be going through changing the text and take a few words or sentences out, and suddenly two instances of "tumbled" will end up within two lines of each other and stick out. This kind of repetition is best avoided because it is accidental and comes across as awkward.
3. References to characters. It doesn't make any sense always to refer to characters the same way. That's what pronouns are for! Generally you'll see references occur in a sequence where the first instance will be the name (or a description like "the man with the yellow hat"), and thereafter you'll see the pronoun "he." If for some reason readers need to be reminded which "he" we're talking about, you may return back to the original name, or a briefer description like "the man" or "the alien." There are times when it's good to repeat, however - if you're in a paragraph where you have multiple characters of the same gender, you can let one of them (the main character) take the pronoun ("she") and have others be "the woman" or "the tall woman"/"the dark-haired woman" consistently to keep it teased apart. Thus, usually you will progress rapidly down the sequence of reduced complexity until they reach the basic pronoun and stick; however, in places where there is ambiguity (two or more characters of the same gender), repetition can be vital to keep readers from getting confused.
Now we come to the place where we find the real words we want to use repeatedly.
4. Talismanic words. These are words that possess "spirit." They are content words, like nouns or verbs, rather than function words. When they repeat, they create atmosphere. "Lamplight." "Pearl." "Darkness." "Typhoon." They can also occur in webs of associated words that all appear when a particular atmosphere is being created. These words can also repeat across contexts to create greater cohesion in a story. You don't want them repeating just any-old-where, but if you pay attention to where you put them, they can create parallels in the reader's mind between different parts of the story. In fact, I find that there is a certain correlation in the use of talismanic repetition with genre. It is more common to find this kind of repetition in fantasy, in my experience, than in science fiction. When I write science fiction I find myself deliberately trying to avoid word repetition, but when I write fantasy it doesn't happen as much. A really wonderful example of an author who uses talismanic repetition is Patricia McKillip. If you look at her books The Changeling Sea or The Tower at Stony Wood (my two favorites) you will see what kind of powerful effect this kind of repetition can have.
At this point I can hear in my mind's ear the voices of people saying, "But science fiction does this too!" I think it does, to some extent. However, it uses different kinds of words - it skews toward the use of alien words, or neologisms, or technical vocabulary. These words possess an atmosphere too - indeed, it is the atmosphere of science fiction! - but if I may speak metaphorically, they are shallower than the words that fantasy uses. Because words access all of their possible meanings in our minds at once, the words that we have heard all our lives resonate deeper into the reaches of our minds, and need less support from the immediate story context in order to invoke their "spirit."
It's something to think about.