EDIT thanks to medina's comment: According to the man page, you should be able to write
ALL ALL = (ALL) NOPASSWD: ALL
to allow all users to run all commands without a password.
For reference, I'm leaving my previous answer:
If you add a line of the form
%wheel ALL = (ALL) NOPASSWD: ALL
/etc/sudoers (using the
visudo command, of course), it will let everyone in the group
wheel run any commands without providing a password. So I think the best solution is to put all your users in some group and put a line like that in
sudoers - obviously you should replace
wheel with the actual group you use.
Alternatively, you can define a user alias,
User_Alias EVERYONE = user1, user2, user3, ...
and use that:
EVERYONE ALL = (ALL) NOPASSWD: ALL
although you would have to update
/etc/sudoers every time you add or remove a user.