when you are working in environment where your network is designed with workgroup, usually we dont put security in such network, but what if all of the sudden some of your computer start to ask for the password whenever you try to access them,
1st thing you can see is, if you have enabled the password protected sharing ,
go to
Control PanelNetwork and InternetNetwork and Sharing CenterAdvanced sharing settings

and then click on your network type, home/work/public ? and then turn off the password protected sharing as shown in the image below.

Workgroup Computers Ask For Password

but in some cases, even if you have turned off this option you still get security popup asking for security credentials, same problem i faced few days ago when i was on a visit to my client , where i have to share some folders between 2 computers, 

Workgroup Computers Ask For Password

i tried to enter the username & password of the target computer many time and even ticked the option to remember my credentials, but after restart it started to ask for the password again,
so how i resolved this issue,
i simply typed the username & password of my own computer ( from where i was trying to access other computer) and ticked the remember my credentials, and it never asked me again for this.