Turns out I can only use git-gutter and git-gutter-fringe, since I'm on Emacs 24.3, not git-gutter+ or git-gutter-fringe+.

Of the two I can use, git-gutter-fringe seems to be the best option since it doesn't take up an extra column in graphical Emacs. It requires git-gutter.

(require 'git-gutter-fringe)
(global-git-gutter-mode +1)

I gather that git-gutter+ and git-gutter-fringe+ add more functionality for staging and and committing directly from the buffer. That's not something I desperately want; I just like the idea of seeing changed lines as I type.