In much of Europe it is 2 hours before, and there is no one at the check-in desk earlier than that.

Just in case this helps anyone, at ZRH (and I assume GVA) you can check bags 24 hours before flight IF on LX or LH (not UA).
Due to evaporated R and I/O inventory out of ZRH, I have found a lot more inventory flying ZRH to FRA/LHR and then onward to the US (on UA) from those gate areas. It's so great to check luggage in a day ahead of time and get BP if connecting in FRA/LHR.