How can you git add a new file without staging it?

With Git 2.5, git add -N/--intent-to-add is actually the right solution.
The new file won’t be part of the next commit.

See commit d95d728 by Nguyễn Thái Ngọc Duy (pclouds) (merged in d0c692263):

diff-lib.c: adjust position of i-t-a entries in diff

Problem:

Entries added by “git add -N” are reminder for the user so that they don’t forget to add them before committing. These entries appear in the index even though they are not real. Their presence in the index leads to a confusing “git status” like this:

On branch master
Changes to be committed:
        new file:   foo

Changes not staged for commit:
        modified:   foo

If you do a “git commit“, “foo” will not be included even though
“status” reports it as “to be committed“.

Solution:

This patch changes the output to become

On branch master
Changes not staged for commit:
        new file:   foo

no changes added to commit

That means:

Treat such paths as “yet to be added to the index but Git already know about them”;
“git diff HEAD” and “git diff --cached HEAD” should not talk about them, and “git diff” should show them as new.
+ files yet to be added to the index.