How can I transfer information using a hard drive?

I need to transfer all of the files from one Macbook to the a new one. I tried the Migration Assistant but the new Macbook doesn't have a Firewire port and a Wireless Connection takes forever so my only option is to transfer all of the information from one Macbook to an external hard drive I have lying around. The problem is, I have files on the hard drive that can't be erased and Time Machine only lets me format the hard drive. Is there any way to make a complete backup without formatting the external hard drive?

Edit: Finally got it to work using an AFP connection. Thanks to erikgil for coming up with this solution and for everyone for trying to help me out.