What kind of electrical appliances can be run on solar?
In case of a grid-tied or grid-connected solar power system the solar power is consumed instantaneously by all appliances that are ON at that time.
In case of a hybrid solar power system, the solar power is consumed by all the appliances that are connected to the solar inverter i.e. connected loads only. The rating & sizing of the solar system components (solar panels, solar inverters & solar batteries) determines the quantity of appliances that can be connected & the extent to which they can utilize solar power. For minimum dependence on grid power the solar power system can be rated to provide solar power even to higher energy consuming appliances, or appliances normally plugged into 15A sockets such as microwave oven, induction stove, hot water geyser, washing machine, air conditioner, water pump etc. In case the solar power system is being designed to provide limited back-up power, then only essential loads or loads normally plugged into 5A sockets such as lights, fans, TV, mixie, fridge, electric iron, etc. are connected to the solar power system.
A comparison of the appliances that can be run by different types of solar power systems can be found here