The simplest way to upgrade the suspension of your Subaru WRX or STI is to add lowering springs, with or without upgraded struts. (Struts are sometimes referred to as shocks.) A traditional spring and strut suspension has many advantages, including long life requiring little or no maintenance, quiet operation, and good wheel and tire clearance.
Note that too much lowering will give bad results. We recommend lowering springs that drop the car by 1.0" or less. If you lower the car too much the stock or stock-style dampers will be over-taxed and the whole suspension will be badly-controlled, resulting in a bouncy ride, bottoming out on the bump stops, and other unpleasant behavior.
Installing high-performance struts can provide a great improvement in handling, especially on the WRX. (The WRX STI is equipped with higher-performance struts, and boasts a fancy inverted monotube front strut design.)
As with other parts of the car, the engineers working on the WRX -- especially the earlier models -- went with a compromise on the factory dampers that favors comfort over performance on the stock vehicle. Firmer shocks are one of the most effective ways to improve the handling of your Subaru WRX. The fancier shocks offer adjustable dampening at the click of a knob. Drive to the track on "soft," crank up to "firm," and humble your unsuspecting competition.