Most monitors don't show colour or grayscale tones correctly. I use Eizo and NEC high end monitors which are hardware calibrated using Basiccolor software and an Eye One device which sits over the screen during the calibration process. This has to be done regularly to keep the displays calibrated to within the tight tolerances needed for my work.
You don't have to go to the length I have if your are not in the imaging business, one simple initial test to see if your monitor is displaying the greys correctly is to view a greyscale step wedge. If you can see a difference in tones between each step from black to white then your monitor has probably already been calibrated, if steps on the scale merge into the next then the monitor will need calibrating or just may not be able to display all the range due to it being a budget version, or just an old one!
Here's a step wedge below to test your monitor. Click on it to enlarge.
There are other factors associated with getting you monitor to display accurately, such as the colours that it is capable of displaying and the environment that your monitor is in. Having a monitor right next to a window or with normal room strip lights above it (or both) will easily fool your eyes when looking at the screen. It is best to have the monitor in a room without natural light, with neutral walls (preferably grey), and any lighting in the room to be as near as possible to daylight. It can help if you replace the warm (or cool) white office fluorescent tubes with ones that are closer to daylight such as Philips Graphica Pro.
The subject of colour calibration and workflow is vast but I hope you have had a little fun in testing to see if your monitor is anywhere near showing the correct greyscale.
