Is it possible to install FreeBSD on a typical home router such as the NetGear DG834G?
Or is there an alternative that is suitable for a home setup?
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FreeBSD only runs* on x86 and amd64 hardware. Since most home routers are using a different kind of cpu (like ARM) it will not work.
You can find a list of supported hardware over here: http://www.pfsense.org/index.php?option=com_content&task=view&id=44&Itemid=50
Personally I can recommend the Soekris hardware, but if you don't have the budget for that than ALIX is a reasonable alternative.
*as corrected by @wormsparty this is not 100% true, it is possible to run on other hardware but having a fully functioning router is a different question