If you have a folder with your FM file it in, and another folder inside that, called My Images, then you will be able to link images in that folder by reference. If you move the complete top-level folder to another computer the images will still be available. But the images will not be available to any other user, in either circumstances (without doing a bit of drive-mapping set-up).
Here is an example file. It has a primary folder containing the FM file and another file named images. It is set up so you can move it, and the links will automatically update.
If you are HOSTing or Serving the DB file using FMP12 and do what Sorbsbuster suggest
No need to worry about filepaths at all.
Changing computers will require users to change their access to the HOST or Sever.
Google "define paths site:forums.filemaker.com" Threads about paths on this Forum
Guide to a cross-platform container field with reference to stored document