We usually only define ##n!## for natural numbers ##n##. Then ##n!## can never be negative. There is however a very natural extension of the factorial, this is called the Pi function (which is just a translation of the Gamma function). This can indeed become negative as you can see from the graph: http://en.wikipedia.org/wiki/Gamma_function
If we extend the domain we can have negative numbers for example -1~(-3.74768264672741260139148848269149969586163939513235551205229915)! -1~(-3.45702473822080062303945414765117954323659790903378442096479450)!