It very much depends on what kind of energy it is, and what we do with it.
Unlimited energy means it has to come from somewhere, and go somewhere.
Solar is the obvious candidate for an unlimited energy world, with the day far away when we ever have any scarcity of solar. But that doesn't mean we'll have unlimited resources of everything else and 100% efficient machines.
Even if we assume every single machine runs on electricity which we can cheaply convert from solar, they'll dump heat into the atmosphere, driving up temperatures. Also, demand for materials will shoot up which enable us to store and utilize electric energy(such as Li-ion batteries).
On the bright side, comfort level of people will increase. Today electricity can be converted to almost any other form of energy - heat, cold, magnetism, fuel, anything. That'll help people get comfortable where they live - and it'll be widespread as even the poor will be able to use the energy.
Mankind will have a more sustainable future than what is there today. We could control or even reverse the greenhouse effect, reduce pollution and eventually eliminate it, build high speed transportation to anywhere in the world, build energy based shields for large scale disaster control.
Another use I can find is high-speed space travel. Assuming we can store and use huge quantities of energy in spaceships(developing the ionic engine concept), we could achieve near-lightspeed travel. That could allow us to inhabit and mine other planets.
So to summarize, it could lead to elevated temperatures(atleast unless we find a way to dump that excess heat), put a strain on other resources as the resource use per capita increases, but aspects of life dependent mostly on the energy we use will see a significant benefit.