This article is pretty inaccurate with respect to the uniqueness of this phenomenon: "What’s unique about her cells is that, not only do they never die, in contrast to normal human cells which will die after a few replications, but her cells can also live and replicate just fine outside of the human body, which is also unique among humans"

Most cells derived from tumors can be "cultured" like this, indefinitely. That's what makes cancer cells cancerous. There are literally thousands of "cell-lines" in regular use by cell-biologists all over the world. HeLa cells are robust and ubiquitous, but definitely not unique. In fact, one can order nearly 1000 such cell-lines from the 'American Type Culture Collection' (ATCC):

http://www.atcc.org/Portals/1/TumorLines.pdf

see also: http://en.wikipedia.org/wiki/Cell_line#List_of_cell_lines