That is going to depend on the device.
For anything with a modern switched mode PSU it probably will (check the information label!) as most smaller ones are duel voltage 110/220 (especially anything portable), but something like a desk fan is usually running at mains voltage with the motor wired basically direct (at most a fuse and RF suppressor) so it'll either be 110v input or 220v input, so a 220v one from the EU/UK might work (albeit slowly) in the US, a US 110v one plugged straight into the 220v UK mains is likely not going to be happy and let the magic smoke out.
I've seen so many reports over the years of people plugging PSU's in and having them pop because until fairly recently whilst most PC PSU's were "duel voltage" there was often/usually (depending on when you're talking about) a selector switch that needed to be set correctly, and UK PSU's didn't always get it set right before it was packed at the factory in the English (UK) box with the UK plug.
Remember it's not just the physical shape of the connection that varies between the UK/EU and US, it's the actual voltage.