While in MiKTeX an installation process is automatically triggered if you have, say, \usepackage{beamer} in a document preamble without the corresponding package installed, there is no such feature on TeX Live.
The last statement is not true actually, as pointed out by wasteofspace in the comments there is the texliveonfly package that implements the on demand installation in TeX Live 2010 and later. I never tested it and don't know if it has drawbacks.
However, if you install the full (or almost full) TeX Live collection of packages (~2400) you will not need to add new packages, a periodic tlmgr update -all will take care of everything, including the installation of packages added to the TeX Live collection after you first full installation. This feature is explained in the tlmgr manual.
Analogously, if a package has been added to a collection on the server
that is also installed locally, it will be added to the local
installation. This is called auto-install and is announced as such
when using the option --list. This auto-installation can be suppressed
using the option --no-auto-install
The manual has lots of info on useful commands and it is a recommended reading for every user.
The downside is of course that you need the full set of packages installed in your machine, which may be a problem if you don't have enough free space. If you really can't spare 2GB from your HD, it is also possible to install TeX Live in a, say, 4GB USB key and live happily ever after :)
Everything I just wrote requires that you install TeX Live with one the methods described here. If you decide to use the TeX packages from your distro you are forced to follow their update policy, which is different for different distros
Best Answer
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 isluatex, experience a delayed release until the work has been done to integrate the MikTeX additions that enable on-the-fly downloads.Outside of the MikTeX distribution, I am aware of no set of TeX compilers that includes the ability to automatically download missing packages. You could try compiling and installing the MikTeX Tools which is an attempt to port the MikTeX package manager, and versions of the TeX compilers that are integrated with it, to UNIX and Linux.
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
tlmgrpackage manager domwass described in his answer.