Basic question. Can you get sick and die from drinking infected brew? I know that it must taste terrible, was just wondering. Can't seem to find any references where people have died from infected beer.
In short, no. Otherwise beer making would have never made it out of the middle-ages.
The acidic environment and low alcohol does a good job of stemming most pathogenic bugs. Certainly some microbial contaminations might not agree with different people and make them ill. The general rule of thumb is that pathogens do not survive in beer, hence why you can't find any references to people biting the dust due to beer contamination.
Botulism toxin is the only "infection" I've heard about in the brewing community that would be potentially hazardous, but it's only a concern for canning wort. If you're not growing yeast starters in home-canned wort, it's non-issue. And even if you are, the topic is often debated.
As I understand it (and I'm definitely no expert), the problem is that botulinum spores (which are in just about everything that grows in dirt) aren't destroyed during normal boiling. Say you boil some wort for canning. Unless you're using a 15psi pressure cooker, the wort never reaches the 240*F mark needed to destroy the spores. The spores themselves aren't dangerous, but they release botulism toxin during reproduction. If you pitched yeast in this wort, the spores would never have a chance to reproduce and you'd be fine. Without the yeast, though, the spores can find themselves in a happy environment (once the wort cools) and begin reproducing. Once released, the toxins produced during by the spores can't be destroyed by any amount of boiling.
That said: it's rare. In fact, I've never heard about it happening. But every thread I've seen about canning wort includes a discussion on botulism. So to answer your question: yes, it is theoretically possible to get sick from a "bad" beer. I think it's more likely that someone would die of alcohol poisoning from too many 'infected' beers than to get botulism poisoning from one.
In the Middle Ages, they used to do things like add chicken broth to beer, I kid you not (I ran into a few recipes at one point). Alcohol itself tends to retard pathogens and if you aren't adding this sort of thing to your beer it is unlikely that you will get the right kind of pathogens growing to make you sick anyway.
Also there are a lot of places today that do wild yeast fermentation (ranging from things like kim chee which involves both wild yeasts and bacteria to some traditional alcoholic beverages). I am actually looking at trying to do this with guanabana in the near future. If it was dangerous, brewing never would have gotten started seriously nor, for that matter, would we eat sauerkraut.
The rule of thumb I've always been taught is that if the beer smells that bad you won't drink it, and anything that simply tastes bad probably isn't enough to hurt you.
That being said, I've never heard of anyone being sick due to contaminated beer, with the exception of dirty beer lines. I've gotten puking sick from dirty beer lines a few times back in the day when I shot league darts.
It seriously depends on what has infected your beer; but, we have a digestive system that has allowed us to eat much less sanitary food than we currently enjoy. Even if you threw a cup of dirt into your beer, you'd probably survive it. Most brewing infections lack a good "starter culture" of truly pathogenic substances.
On the other hand, life is to short to drink unpleasant things in the name of fun. Since someone mentioned this is your second question about sanitation. You need to focus on the slighly-less-fun side of brewing, washing.
B-brite on everything with scrubbing until it appears clean. Replace items that have unnecessary seams that can catch food / liquid with ones that don't (that means the cheap-looking "one piece" spoons are actually better, etc). Rinse with iodaphor solution, not water.
Yes you could get sick from some bad brew, but typically you'll stop drinking bad tasting stuff before you overload your body's defenses, and you probably won't encounter most waterborne ailments (in concentrations that will hurt you) unless you are starting with a very unsanitary water supply (cholera, etc). Even then, the alcohol will do it's best to kill of the pathogens, and it usually works pretty well.
In short, no. As far as I know, most "infected" beer is a version of vinegar. Even something that is vinegar in smell and taste is difficult to drink so if it's really infected to the point of causing deadly illness, it's unlikely that you'll be able to stomach enough of it to cause anything beyond a stomach ache.
I still stand by the rule that sanitation is the most important step in homebrewing!