As far as I can tell, there are only 3 categories of evidence which support the CAGW Hypothesis:
(a) It is possible to construct a simulation which is consistent with many historic aspects of the climate and which also predicts a lot of warming in response to increases in atmospheric CO2;
(b) Certain aspects of modern weather/climate are unprecedented; and
(c) Many prominent scientific bodies have endorsed and accepted the CAGW Hypothesis.
I will deal with each of these in turn.