An easy solution would be to install the same version of MySQL on the destination computer and copy the 'data' folder from the previous computer to the new one.
Thorpe was probably going to suggest you dump the structure & data of all your DB's to .sql file(s) and re-create them on the new server.
His method would probably be the preferred one, but I don't see why copying the data folder wouldn't work as well (assuming you install the same version of MySQL), as I have done this in the past.
If anyone has warnings/suggestions as to why you shouldn't do this, please post!
