In June, 2002 a part-time caretaker in a Toronto school was rushed to hospital after complaining to a co-worker that she was unable to breathe. She later died in hospital. Investigators looking into the incident discovered that she had mixed a sanitizing product containing sodium hypochlorite with an acid toilet bowl cleaner. The two ingredients had reacted together to form deadly chlorine gas, which led to her death.
It's an extreme case but it's an example of the health hazards that can be associated with chlorine bleach, or sodium hypochlorite. When bleach is mixed with acids (typically found in toilet bowl cleaners), it reacts with them to form chlorine gas. When it is mixed with ammonia, it can create chloramine gas, another toxic substance.
In the environment, sodium hypochlorite is acutely toxic to fish. The chlorine in bleach can also bind with organic material in the marine environment to form organochlorines, toxic compounds that can persist in the environment.
There may be some circumstances where bleach use is necessary for disease control, but there is little need for it on a regular basis. Tests have shown that washing counters and other surfaces with soap and water removes most bacteria and there are a number of oxygen-based alternatives for laundry uses of bleach.