yes, this is possible..what you want to do is image/mirror the drive. There are software products that make this process easy. What type of drive is the new one? If its a maxtor, I'd recommend there software...
oopss...just realized you may not want all of the system files/etc...but just select data. If thats the case, you have a couple options. You can temporarily hook up the new drive as a slave to the drive on the old system and just drag/drop the files you want, then connect the drive back to the new box (just remember to reset the drive to master).
If you can network the two its even easier--what OS are you using? if its w2k, just right click the drive, select sharing, and select share drive. Then map the old drive on the new computer and again, just drag and drop..
hope this helps..