Going to assume your referring to USB 2.0?
I would avoid recording to the internal drive of your computer. Unless you know your drive can move both the OS info and the audio in and out fast enough...
You can certainly record to a USB drive, but like Mr. June said, you will run into issues with the computer being able to move data fast enough.
If you have a desktop, see if you can put in a second SATA drive internally to record to,
(you can do the same for most laptops if you want to ditch your CD drive) (Just put a SSD for my boot drive, and my laptops wicked fast. The other HDD is now in the CD bay for recording onto when I don't use external drives.)
I personally have two FireWire 1TB drives for recording to, and then several other USB drives for backup. My opinion is that until Thunderbolt or USB 3 are more widely available, that FireWire is the way to go. I could be completely wrong, but that's what I am sticking to.
It all also depends on what you want it for really.
If your doing just a few tracks, you could get away with the internal drive.
But once you start piling them up you may find that the computer wont be so reliable when recording.