Note that Mac OS/X, though it is also a Unix-based system, has different options; users should refer to the information in Mac systems.
The TeX distribution of choice, for Unix systems (including GNU/Linux and most other free Unix-like systems) is TeX Live, which is distributed as part of the TeX collection.
TeX Live may also be installed “over the network”; a network
installer is provided, and once you have a system (whether installed
from the network or installed off-line from a disc) a manager
tlmgr) can both keep your installation up-to-date and add
packages you didn't install at first.
TeX Live may be run with no installation at all; the web page TeX Live portable usage describes the options for installing TeX Live on a memory stick for use on another computer, or for using the TeX Live DVD with no installation at all.
TeX-gpc is a “back-to-basics” distribution of TeX utilities, only (unlike TeX Live, no “tailored” package bundles are provided). It is distributed as source, and compiles with GNU Pascal, thereby coming as close as you're likely to get to Knuth's original distribution. It is known to work well, but the omission of ε-TeX and pdfTeX will rule it out of many users' choices.