Many stars are very far from white! The reason one may get the impression they are all white is just that our color vision is pretty bad when looking at dim objects. However, even with the naked eye, you can clearly see a whole variety of colors on a dark night. For instance, Betelgeuse can be found on the shoulder of Orion, and it is clearly red. The brightest star in the sky, Sirius, is notably blue. My favorite example of diversity is the binary system of Albireo. You need binoculars or a telescope to separate the two stars, but then you clearly see one as bluish and the other as orange. A southern sky equivalent would be the Jewel Box, though I have not seen that one personally.
In fact, stars have a color index associated with them. Basically, you take a star's luminosity in two different, standard, narrow-ish bandpasses - such as B (blue) or V (visible or green) - and take the logarithm of the ratio of luminosities. In the B-V case, a larger number means a redder star. Sirius is about 0 on this scale; Betelgeuse is almost 2.
Note that because stars are roughly blackbody emitters, you won't see every color. Blackbody spectra form a one-parameter family, usually parameterized by the effective temperature. Take the emitted spectrum at a given temperature, convolve it with a response function for human vision (something people still debate the details of), and you get the perceived overall color. This image shows roughly what colors you might see a blackbody as. This is the same phenomenon behind glowing hot metal, so the colors are much the same. Note that the curve traced out by various temperatures happens to miss the green region - you will never see a green star. Once stars are hot enough to be emitting more green than red, they are emitting enough blue to appear white-ish.
