If you are running vista try right clicking the shortcut icon and running it as administrator.

It might be the old vista 'relocating non-admin data' trick then. Have a look in
C:\ Users \ <username> \ AppData \ Local \ VirtualStore \ Program Files
your saves may well be in there and I think you need to be running as an admin to access that folder

Yea thats what I figured it might be.

In Vista applications are no longer allowed to alter data in their own application folder. For compatibility anytime a program tries to do this it copies the file to:
Users\<user name>\AppData\Local\VirtualStore\<app folder>
So when you run JA2 in non admin mode it starts saving all your saves to the above folder. When you run it in admin mode it starts looking in the normal folder in Program Files though. Just copy them to the main folder and it should work.

I have Windows 7 64 bit and when I try to load a saved game, it stops about halfway through loadingf

As was mentioned before, this is due to installing the game in a protected location. Move the game's folder outside of Program Files (x86), grab your saves from "%localappdata%\Virtualstore\Program Files (x86)\GOG.com\Jagged Alliance 2" and run the game again.
Alternatively, always run the game as administrator, though you will have to move the saves first.