*Is this the only one or are there others defined by other sign conventions?*

As has already been mentioned - there are essentially two but the Koszul one is amongst other things, the only one which makes the tensor product of complexes a complex.

Since I have been interested in this topic of late, I would point you towards the following internal (within MathOverflow) references:

For a recent discussion see MathOverflow question:
http://mathoverflow.net/questions/93464/tensor-product-of-linear-mappings-versus-chain-complexes

In particular Simon Letner and Qiaochu Yauns' answers provide a nice conceptual backdrop.

I also found Theo Johnson-Freyd's answer in this MathOverflow question quite illuminating:
http://mathoverflow.net/questions/53315/references-for-sign-conventions-in-homological-algebra

Theo Johnson-Freyd's answer in this thread is also instructive:
http://mathoverflow.net/questions/95795/sign-convention-for-derivations-in-cdgas