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Interesting question. I found a link here that is quite outdated, but I think it gives a helpful breakdown (http://www.itproportal.com/2007/10/30/survey-reveals-most-popular-server-operating-systems/). It lists the popular servers of '07 as:
Red Hat 15%
Notice that the list is dominated by linux variants. The Windows vs. *nix argument aside, one of the driving factors in hosting is licensing cost. Windows licensing takes the cake here. I imagine that CentOS has jumped up in market share as well because it's essentially a license-free Red Hat variant. I would guess that FreeBSD hasn't moved up at all, and Gentoo has moved down if anything. One distro you don't see on this list is Ubuntu, which undoubtedly has a pretty good market share as well.
Overall, linux is the victor. Years ago I remember HP switching over internally from their own HP-UX unix to Linux. Certain divisions just couldn't get around the price, despite it being their own product.
Nice response. I was pretty sure that it was Debian. I believe I read that Ubuntu is becoming a popular Debian server distro (I'd cite the magazine, but I can't recall which one. I think it was Linux Format from a few months back, but I won't swear on it.)