It is smart to do some research before you undergo a procedure.
There have been numerous long term studies of silicone breast implants. None of the studies have been able to show that silicone implants cause any kind of illness. The implants themselves are safe.
If someone develops a problem, it is not because of the implant itself, but because of something related to the surgery. One problem is called "capsular contracture." This happens when the scar around the implant becomes excessively tight and begins to distort the appearance of the breast. This happens to 5-15% of women and nobody understands exactly why it happens. Most of the time, it can be taken care of by removing the tightened scar.
Other problems like infection, bleeding and wound healing issues do happen also, but these are rare. Plus, these are problems that happen with any kind of surgery, not only breast augmentation.
The most common issue is probably dissatisfaction with the result. Some women may want a bigger size or a different shape. This can be avoided by a careful and thorough consultation with the surgeon. You should be able to describe exactly the kind of result you want. Also, the surgeon should explain exactly what he/she thinks can be accomplished.
It is extremely rare to have some kind of debilitating complication from having silicone implants.
In general, if you find a nice doctor, with good before and after pictures, who listens to you and is Board Certified, then you will probably have a very positive experience and result.