Just like any restrictive thing there are risks... If the binder is /to/ tight than it can cause some problems but nothing like cancer. Cancer is caused by a pre-disposition to the disease, not by applying pressure to your chest.
The few issues I've had first hand is some nerve and circulation issues when I used only ace bandaging before I owned a binder, as well as with the binder I have which is to small. I can feel my hands swelling and going numb after about an hour, so make sure the binder isn't so restrictive it cuts off proper circulation.
Also, just like with things such as corsets over time constant wearing of a binder will start to modify ones body. If the binder is restrictive enough over time it may start reshaping your ribs.... but this is a very minor as the time it takes for something like a binder to do such modifications takes a very long time.
As stated the worst I've had is circulation and nerve(one was cutting into my syatic nerve which caused issues for weeks after) issues for wearing a binder which is to small, as well as some bruising of the tissue around the tightest points.
Make sure to give your body a few hours rest from the restrictions and don't sleep in a binder and you shouldn't have any troubles.