That depends. Anything with a transformer will not work on DC. Some power supplies don't have a transformer directly connected to mains and they will just work. A large number of appliances use universal motors (anything in your kitchen) and so they will just work. Heaters are typically just resistance and again will just work.

However there are a lot of things that won't work on DC as well. Since very few people are running mains voltage DC labels often will not tell you if it will work. (I've toured ships with mains voltage DC and those outlets are labeled - I assume the crew is trained - or perhaps was since this is just a museum now and I'm not sure if current ships use DC)