Can your health insurance company raise your rates after you get sick?

I've heard about pre-existing conditions and all, but what about getting seriously ill AFTER you have insurance? Let's say you're generally healthy, and already have heath insurance which you pay for yourself, at a reasonable rate. Then you get a long term illness, or get into a terrible accident, and need years of expensive care. Of course you keep your policy up to date... Can the company raise your rates by triple (or worse) if you get sick this way?