Depends on the model of your Xbox 360 and the model of your monitor.
If both have HDMI, your life is easy. Plug the HDMI cable into the console, then another end into the monitor. Done. If your monitor is a lower resolution than the TV previously used for the Xbox, then you may get a blank screen. Turn the console on, and hold "Y" and "Right Trigger" as the console boots to reset the video settings to default. This should get it to display.
If you have a HDMI Xbox and a DVI monitor, then you can use a HDMI to DVI cord. Very inexpensive.
If your Xbox doesn't have HDMI and instead uses only composite (yellow/red/white) or your monitor only has VGA, you will need to purchase an adapter box to convert the signal properly. Again, very inexpensive some place like Amazon.
So, in short, yes. You just may need some extra bits to make it work.