(late edit for a feature added in Git 1.8.5, after the question and answer were written:)
Git’s pathspecs ordinarily match * with any path substring, including / separators, but you can use shell pathname-matching conventions by adding a magic :(glob) prefix. So to list just the files in the current directory,
git ls-files ':(glob)*' # just the files in the current directory
git ls-files ':(glob)test/*' # and so on
As a side note, you can do many more things with those magic prefixes, chase that link.
You can also turn on shell-style globbing with the --glob-pathspecs option on the Git command itself, so
$ alias ggit="git --glob-pathspecs"
$ # and a personal favorite:
$ git config --global alias.ls 'ls-files --exclude-standard'
$ # then whenever
$ ggit ls '*' # note the quoting to bypass the shell's globbing,
Original answer, still works:
I think you want git ls-tree HEAD sed’d to taste. The second word of ls-tree’s output will be tree for directories, blob for files, commit for submodules, the filename is everything after the ascii tab.
Edit: adapting from @iegik’s comment and to better fit the question as asked,
git ls-files . | sed s,/.*,/, | uniq
will list the indexed files starting at the current level and collapse directories to their first component.
Further edit: another way to do it is
git ls-tree `git write-tree` .
and you can use git ls-tree‘s options for some nice seasoning.