Probably a videocard driver issue. I doubt the IP-block solution some mentioned as there shouldn't be any DRM in the GOG.com release.
http://www.gog.com/forum/assassins_creed_directors_cut/ac1_frequent_freezes_fixed
http://www.gog.com/forum/assassins_creed_directors_cut/assassins_creed_crashes

Unfortunately it has. The DRM-free Amazon version has the IP problem as well. The game tries to contact a dead server.

@Alexrd
Indeed, I switch off the network, and AC works!
So does this means AC has DRM incorporated???

Apparently yes, lthough I'm not sure it can even be considered DRM. Either way, it shouldn't be present on an allegedly DRM-free version.

P.S: If you don't want to turn off your internet connection to play the game, add the following IP addresses to the "hosts" file on "C:\Windows\System32\drivers\etc":

216.98.48.18 127.0.0.1
216.98.48.53 127.0.0.1
216.98.48.57 127.0.0.1
216.98.48.133 127.0.0.1
216.98.48.134 127.0.0.1

Thanks!

But why doesn't GoG fix this?
They always preach "No DRM in our games" and than this!

This needs to be stickified.

Well, in fact it's a problem that shouldn't occur in the first place and should be fixed but for now this HAS to be a sticky.

It´s not a problem anymore:
If you install the latest Nvidia-Driver and do NOT install Nvidia Update this problem is completly gone!

Given that a large draw of GOG is that games are generally pre-patched and do not require any workarounds on the part of the user, this is still troubling. Add in the fact that the source of the problem appears to be a form of DRM in a game that is supposed to be DRM free, and the whole thing stinks that much more.

It´s simple a problem between the game and Nvidia Update, nothing more:
Cause Nvidia Update is quite a shit this shouldn´t be a problem ;)

I wouldn't exactly call it DRM, since the game never had an internet connection as a requirement (even before it arrived on GOG). Not to mention that it has been confirmed to be a drivers problem.