I brew a whole pot for myself and then refrigerate it (I drink it black). It usually takes me about 5 days to finish the pot. If I stretch it to 6 days, sometimes the last cup tastes "tinny" (metallic) and I don't enjoy it very much. Funny thing is, the freshly brewed (first day) cup is "just okay" as it tastes more tannic than the cups I have on day 2 through 5. Having it "mellow" in the refrigerator seems to make it taste smoother to me and I enjoy it more. I heat a single cup of it up in the microwave each morning. From reading other's comments, I can see I'm not with the crowd as most people detect a negative taste from coffee after just a few hours from brewing. Frankly, I like coffee most ways. I like the $6 hand-poured stuff where you can really taste the beans, and I'm fine with most diner coffee too (as long as its not too watery). I just feel its a waste to throw away coffee that's been brewed just because its not "fresh." In my opinion, it just tastes different, but not "bad."
To answer the actual question; I don't really know how long its safe, but almost all food is safe in the refrigerator for several days (as long as its not been sitting out too long) and in my years of experience with coffee, I feel comfortable with keeping it up to a week.