you sure can!! My favourite way to shoot pictures..I looove b&w! You need to be in manual mode, then go into your shooting menu, under "set picture control", and put it on monochrome.
You really don't need to use a filter with the D90 for B&W. You can also convert any picture you have taken with the D90 to B&W in post production. In essence, any picture you take can be captured in color and then have a color and B&W copy. On page 210 of the user manual it talks about "Creating retouched copies"of photos. Then on page 214 it tells you about converting to B&W. The next page (215) talks about filter effects the camera will do for you.
Good luck.
Mark
Kevin - Which post processing program you use can impact a B&W shot in camera. If you shoot it in raw and down load it to a third party PP program, like Adobe or Apple then the picture comes out in full color. In order to get a raw B&W shot in camera you will need to download it to a Nikon program like NX2. However if you shoot the B&W in camera using jpeg then it will make no difference which PP program you use it will remain B&W. Hope this helps.