I'm transferring my hosting from another host to GoDaddy. Is there any easy way to transfer the add-on domains that I have (~40) to GoDaddy or do I have to set them up 1-by-1 manually?
Welcome to GoDaddy Community!
There isn't currently a way to add multiple domains to a hosting account. You would need to add them individually. If you're using cPanel with your current host and are moving to a cPanel account with us, this article may help.
Does anyone in the community have have experience moving multiple websites at once? How did you do it?
It depends on the details.
Are you transferring the registration as well as the contents of the web site? Transferring the domain names might be easier than transferring the contents but they are separate problems with separate solutions and perhaps should be separate questions.
To transfer the contents, one possibility is to download the web sites, as if to back them up and/or to edit them locally, then upload them to GoDaddy. How you do that might depend on the hosting plan of the other host as well as your GoDaddy plan. You might be able to use just one download and one upload.
It also depends on what you mean by "Add-On Domain". If you mean sub-domain (as in subdomain.website.com) then that is also different.
For domain name registration transfers use Bulk Domain Transfer | Our Bulk Domain Transfer Tool - GoDaddy. Enter the domain names then press Go then you will get an option to do the transfers.