Several proofs are here:
http://www.maths.ed.ac.uk/~aar/jordan/index.htm
Among them, Tvelberg's Tverberg's (1980) could (and should) be mentioned.
But, after reading (and reading)
http://www.math.sunysb.edu/~bishop/classes/math401.F09/HalesDefense.pdf ,
I really like Jordan's proof itself.

