Generally speaking, increasing ISO will not really improve the quality of your shots. Higher ISO means more noise in most cases, which can drown out details. The story is a little more complicated than that, however. To put it simply...if you can't get a shot at the lowest ISO, increase it. Getting a shot at all is certainly "higher quality" than missing a shot because you cant set a high enough shutter speed.
Let me give you a little bit more background on what ISO is, and hopefully that will help you make the appropriate decisions on your own as to when you might use a higher setting. ISO determines the sensitivity of your camera's sensor. Another way to put it is the ISO setting indicates how rapidly your sensor gathers light...the higher the number, the more rapid it gathers...the more sensitive it is.
Exposure is a triad, and is composed of three different settings working in concert to produce an image: aperture, shutter speed, and sensitivity (of film or a digital sensor.) ISO settings are rated in stops, just like aperture and shutter speeds, so adjusting it has the same proportional effect as adjusting one of the other two settings. If you are shooting with an aperture of f/16, a shutter speed of 1/100, and an ISO of 100, you can adjust any two settings and maintain proper exposure. Here is a table of various one-stop changes that produce the same exposure:
A | S | I
f/16 | 1/100 | 100
f/11 | 1/200 | 100
f/16 | 1/200 | 200
f/22 | 1/50 | 100
f/22 | 1/100 | 200
Generally speaking, you will want to keep your ISO setting as low as possible (usually 100, sometimes it may go as low as 50) to minimize the noise produced by your sensor. There are occasions, however, where using an ISO 100 setting is simply not possible. This usually occurs for one of two reasons (or possibly both in concert): you have your aperture wide open and there just isn't enough light to get a stable shot, or you are shooting action and need a very high shutter speed. In low-light conditions, increasing shutter speed will generally allow you to get a shot, but you are also most likely to get additional noise as well due to the low signal-to-noise ratio of darker pixels. In better lit action scenes, increasing the ISO setting will allow you to use a higher shutter speed than may normally be possible, improving your chances of stopping motion.