Browse computers on network domain

We have finally moved out of the mid-90s and changed from an NT server to Windows 2003 server. The problem is that unlike our old domain, we often have to login in to other computers on the network, something that never happened before. It’s a big hassle when trying to print, for instance, or work on a program with data on multiple computers that it can’t access until we login to it.

I think there must be a setting in 2003 server to bypass the prompt. Does anyone know what it is?
Thanks