If you do a straight copy of the entire partition (not just copy/pasting the files), you still need 2 things afterwards to get a bootable system:
- the MBR bootloader
- mark the copied partition as "active"
There are commands to install a new MBR from a Windows disk (see Chris's answer), but my favorite is to simply copy the first 440 bytes from sector 0 to the new drive via a hex editor. Download HxD, make sure you run it as Administrator, then manually copy/paste the fisrt 440 bytes of sector 0 on your existing hard drive to the new hard drive (in HxD, each row is 16 bytes long, and each sector is 512 bytes). Don't forget to hit save to commit the changes. Be very careful with this, as you can seriously mess things up if you don't know what you're doing.
For point 2, you can accomplish that using the diskpart utility, or again, using your hex editor to mofidy the correct byte. For the diskpart method, open a command prompt (as administrator), then type the following commands:
diskpart
list disk
select disk # //pick the new disk from the list above
list partition
select partition # //pick the C drive
active
Then, go ahead and stick the new drive in and boot it up!