Yes, other companies should follow the example of Google and run entirely on renewable energy when possible. Climate change poses the most severe existential threat to the future of our species and our planet. Companies, especially wealthy ones, should do all they can to transition from fossil fuels to alternative energies.
The main emphasis of climate change action in the past few decades has been on the role of states. However, this is not always within the nation's control depending on the power that private business is afforded within their country. If large multi-national companies such as Google begin to pull their weight it could go a long way to reducing emissions worldwide and removing the pressure from national industries.
Google is being a great example on the future of energy production and use. More companies should strive to run more off of renewable energy. This is a win - win for multiple sides. The company can save money (at least in the long run) by using things such as solar panels for electricity. It would also support companies research the technology and hopefully further the science of it. It is also a win for those companies already producing renewable energy.
The problem with energy is that it is hard to store. Thus, with renewable energies such as solar, wind and water, as unpredictable as they are, it is hard for a company to run entirely on renewable energy. Google is likely doing that for public relations purposes, but not every company has as much money as google.