I did this once. There's probably an easier way, but I just created a folder on my desktop, opened up my ftp client, and downloaded everything in my html folder and subfolders to the folder on my desktop. Then I switched to my new website via the ftp client, and uploaded all of the folders.

Remember to change all the urls in your php, cgi etc files/scripts to your new paths.

I'd suggest wget

More on wget from the Dreamhost Wiki

You friendly with the unix shell at all? If so, log into your dreamhost account and do one of these:

tar -cvzf nameofbackup.tgz ./directorysitelivesin

Then copy the resulting file into whatever your destination root directory is and reverse the process:

tar -xvzf nameofbackup.tgz

If your target platform doesn't support tar or gzip (e.g. Stupid Windows Box), you could go with "unzip" rather than "tar", though I don't remember the syntax for unix unzip off-hand.

(Also note that if your site is HUGE, disk-wise, DH might crap out trying to create the tar file. Freakin' DH.)

there's a feature in dreamhost's webftp that does exactly what you're looking to do, but it has a tendency to hang or even error out if the directory you're zipping is on the large-ish side.

Thanks for the help everyone. I tried using dreamhosts webftp but it froze up. Manually downloading the site to my computer and then using Dreamweaver's Synchronize worked in the long run.