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 network- or offline-installed) 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 e-TeX and PDFTeX will rule it out of many users’ choices. A free version of the commercial VTeX extended TeX system is available for use under Linux. VTeX, among other things, specialises in direct production of PDF from (La)TeX input. Sadly, it’s no longer supported, and the ready-built images are made for use with a rather ancient Linux kernel. Finally, the developer of MiKTeX has released a port of the PDFTeX executable from of that excellent (Windows) system for use on Linux; get it via the MiKTeX site. The MiKTeX package manager (mpm), for Linux, is also available from the same place.
This question on the Web: http://www.tex.ac.uk/cgi-bin/texfaq2html?label=sysunix