Yes, you can run a house completely on solar power in many cases. However, solar power is not necessarily a viable solution for every home.
You should first consider:
The amount of electricity you currently use on a monthly basis
The amount of sunlight your home receives
Whether your roof can accommodate solar panels
If you have excessively high energy needs and/or live in a heavily shaded area, solar panels may not generate enough electricity to run your home. Similarly, if your energy needs are normal but you have limited rooftop space, your solar system output will be greatly reduced.