By the end of every summer it seems like the grate of my charcoal grill is rusty. Does anyone know how I can keep it from rusting and whether or not the rust is unhealthy?
Rust isn't bad for you, with the possible exception of men who have hemochromatosis. Even then, I don't think that the uptake from iron oxide is very high.
The reason rust forms is due to the high heat the grate is exposed to. Unprotected iron will rust when exposed to the air, and the speed at which it does so is dependent on heat (and moisture). So as the heat increases the rate of oxidation increases significantly. Moisture in the air also causes the iron to rust more quickly, as does the moisture in food as it is cooked.
To remove the rust, use a wire brush before and after each cooking session. Applying a layer of oil to the grate before/after cooking on it will help to keep the rust off. In time, you can (depending on the exact composition of your grill) develop a "seasoning" coating on the metal similar to what you would develop in a cast iron skillet.
Are you covering your grill when not in use? If not, it's likely getting rained on/in, which will lead to rust. Another issue might be condensation from the humidity this summer, but I haven't seen that lead to rust in my personal experience.
As far as I understand it, the rust won't hurt you, but it may change the taste of food cooked on it, so you probably want to get rid of it.
We cover our grill after use, and have never had a rust issue, but I know another effective way to prevent rust is to keep the grates oiled. I always wipe down the grates with an oiled rag or in a pinch, a ball of aluminum foil before and after cooking, but you can also get a small spritzer bottle, fill it with vegetable oil, and spray it down. This should help prevent rust going forward. Do not spray oil on the grill while it is on, it will flair up and you will burn yourself!
Some people also don't clean their grates regularly, because the fat from previous meats' cooking is supposed to help prevent rust. This is the "least active" method of rust prevention, if you're going to go this route I would recommend leaving your grates dirty after cooking. Then after you pre-heat the grill, before putting your food on, give it a wipe down with a wire/bristle grill brush to get off what you can, assuming you prefer your grates clean before cooking. They'll get dirty again as soon as you put your food on, then just continue this cycle :)
The problem that I've seen is that you just can't treat your grill grates like a cast iron pant -- the high heat will bake off any protective oil.
For my most recent POS grill (propane, not charcoal), the grates were enamel coated so managed to survive a dozen or so uses, but the burners get so damned hot that they've cooked off the enamel, resulting in rust forming in a nice little line along the grate.
I think this is the same problem that my step-father ran into on his grill, as well.
Your best bet is cleaning and oiling after each use (which I admit, I don't do), and not cooking over too hot of a flame (which again, I don't do that one either).
I have no idea if some brands's grates hold up better to this problem than others, or if we're just expected to replace them every few months. (or years, I've had grills that lasted years without rust problems)
As @IMHO has stated, stainless-steel grates are the most effective way to avoid this problem. I have a set of stainless-steel grates for my weber kettle and smoker, they've never rusted and I even clean them once a year in the dishwasher. (Yes, they do fit - just barely.)
They are a bit more expensive, but are worth the investment, as they are more durable, longer-lasting, and require less effort to maintain.