The weird thing, a lot of digs in Israel and elsewhere in former Biblical lands are more or less privately funded; it's even pretty easy to find digs where you can participate for the price of a (very expensive) luxury cruise, meaning you're paying for the privilege of moving a lot of dirt under a blazing Sun, and maybe, possibly, unearthing an artifact (which will probably be a featureless potshard).
And yes, if I had the money, I'd be doing that right now. ;')
Join a dig, BAR list:
http://www.bib-arch.org/bswbDigBAR.html
Join a dig, AO list:
http://www.bib-arch.org/bswbDigAO.html
2005 summer study abroad programs:
http://www.bib-arch.org/bswbDigSumstudy.html
BAR dig scholarships:
http://www.bib-arch.org/bswbDigScholar.html
Archaeology mag fieldwork opportunities:
http://www.archaeological.org/webinfo.php?page=10015