automationinstallingmactexpackages

Is there a LaTeX distribution for the Mac which has or comes close to MiKTeX's ability to download missing packages automatically?

MikTeX can download packages on-the-fly due to custom additions to the source code used to build compilers such as pdftex. The downside to this approach is that new compilers, a recent example is luatex, experience a delayed release until the work has been done to integrate the MikTeX additions that enable on-the-fly downloads.
Sticking with MacTeX is probably still the best way to go for a complete, stable TeX distribution on OS X. Since MacTeX is based on TeX live and not MikTeX, you won't have on-the-fly installation; but you will have the excellent tlmgr package manager domwass described in his answer.