The climate of the Earth has exhibited both dramatic changes and implausible stability over the last several billion years. We have good reason to think that the Sun was a lot dimmer 4 billion years ago, but we had liquid water even then. We have had icy periods like the ice ages and relatively cool periods like today and much warmer periods too, but we have stayed in that liquid water, life supporting range. So what factors have controlled and varied that climate while keeping it in the habitable range?
It's clear that there are several such factors, but in his 2009 Bjerknes Prize lecture to the American Geophysical Union (AGU) Richard Alley argued that the paleoclimate record overwhelmingly supports the notion that atmospheric CO2 is the big knob in that control system. He supports his argument with extensive data and logic. No one has yet figured out how to explain the climate of the planet without invoking the importance of the CO2 greenhouse.
More recently, A Lacis, et. al., (2010) calculate the response of the atmosphere to removal of the non condensable (CO2, NH2, etc) without directly changing the H2O greenhouse gas concentration. They then put the data into a climate model and allowed it to evolve for a few years. The graph below represents the main results. My favorite line is the black dotted line representing Top of the Atmosphere radiation imbalance.
Notice that removal of the CO2 and minor noncondesibles produces an immediate radiative imbalance of more than 30 Watts/m^2. That is a huge number, and it comes purely out of radiative transfer. No complex climate dynamics are involved - though they come into play in it's later evolution. The longer term changes come out of a climate model, of course, but given the magnitude of the original radiative balance change, are highly plausible. Notice that column water vapor gradually declines by a factor of ten, a completely unsurprising change given the direct cooling and the positive temperature feedback, thus dramatically reducing the crucial H2O greenhouse effect.