Can I connect and disconnect a SATA harddrive while my computer is running?

As long as its not the OS drive you should be fine, since SATA is "hotswappable" though i have experienced corruptions of the FS once or twice. So i try to avoid it.

1. Open your run box, then type regedit and press Enter.

2. Go to the following key:

   HKEY_LOCAL_MACHINE/SYSTEM/CurrentControlSet/services/
   

3. Find 'msahci', click on it and on the right pane, right click the 'start' property.

4. Change the value to '0'.

5. Restart your computer (important)! Now you can 'safely remove' your SATA internal hard drive like you do with external hard drives.

I just did it with a 2 TB SATA 6GB/s hard drive. I am going to try my 3 TB hard drive as soon as I'm done moving data. Just don't forget to initialize in the Disk Mangement window for Windows, then format to NTFS.

Note: I did not hot swap my OS drive as I see that as a bad idea