There's a lot of scientific evidence supporting AGW:
A. CO2 emissions are increasing (causing global warming). In 1870 the amount of CO2 in the atmosphere was about 290 ppm. As of 2010, the amount of CO2 in the atmosphere has risen to 390 ppm. As explained below, very carefully calibrated measurements have confirmed that humans activities are the primary cause of this increase.
http://www.esrl.noaa.gov/gmd/ccgg/trends/co2_data_mlo.html#global
Since the industrial revolution, we've been burning fossil fuels and clearing/burning forests at an unprecedented rate. Through the measurements of specific carbon isotopes, we know these activities are the primary cause of increasing atmospheric CO2.
There are 3 different carbon isotopes: 14C, 13C and 12C. CO2 produced from burring fossil fuels and clearing/burning forests has a unique isotopic composition. This is because plants prefer lighter isotopes, that is they prefer 12C vs. 13C. Thus, plants have lower 13C/12C ratios. Fossil fuels are derived form ancient plants; therefore, they also have a lower 13C/12C ratio. When fossil fuels are burned, CO2 from these ancient plants is released into, and mixes with, the atmosphere, thereby lowering the average 13C/12C ratio of the atmosphere. Scientists have documented lower 13C/12C ratios in tree rings, ice cores and ocean samples; a result of the decreasing atmospheric 13C/12C ratio:
http://www.realclimate.org/index.php/archives/2004/12/how-do-we-know-that-recent-cosub2sub-increases-are-due-to-human-activities-updated/
B. CO2 is greenhouse gas. Increased CO2 will, in theory, lead to an increase in the greenhouse effect. Satellites have measured a decrease in outgoing longwave radiation and ground stations have measured an increase in downgoing longwave radiation, proving there has been an increase in the greenhouse effect. Studies have also shown a direct correlation between anthropogenic greenhouse gasses and the observed increase in the greenhouse effect.
http://landshape.org/enm/wp-content/uploads/2009/01/philipona2004-radiation.pdf
http://www.agu.org/pubs/crossref/2009/2009JD011800.shtml
http://ams.confex.com/ams/Annual2006/techprogram/paper_100737.htm
http://journals.ametsoc.org/doi/abs/10.1175/2008BAMS2634.1
D. In theory, an increase in the greenhouse effect would lead to stratospheric cooling. As the lower atmosphere warms due to an enhanced greenhouse effect, the upper atmosphere is expected to cool as a consequence. The simple way to think about this is that greenhouse gases are trapping heat in the lower atmosphere. Since less heat is released into the upper atmosphere (starting with the stratosphere), it cools. Many studies show the stratosphere is cooling.
http://www.geog.ox.ac.uk/~mnew/teaching/Online_Articles/jones_et_al_attribution_3d_GRL_2003.pdf
http://acd.ucar.edu/~randel/SPARC_revised.pdf
E. In theory, global warming would lead to an increase in the tropopause height. The tropopause is the atmospheric boundary between the troposphere and the stratosphere. Because the troposphere has warmed and the stratosphere has cooled, the tropopause has risen several hundred meters over the past 3 decades.
http://www.sciencemag.org/cgi/content/abstract/sci;301/5632/479
F. Arctic sea ice is declining.
http://nsidc.org/data/seaice_index/images/n_plot_hires.png
http://psc.apl.washington.edu/ArcticSeaiceVolume/images/BPIOMASIceVolumeAnomalyCurrent.png
G. Glaciers are retreating almost everywhere around the world — including in the Alps, Himalayas, Andes, Rockies, Alaska and Africa.
http://nsidc.org/sotc/glacier_balance.html
http://www.geo.unizh.ch/wgms/mbb/sum08.html
H. Ice sheets in Antarctica and Greenland are losing mass:
http://climate.nasa.gov/keyIndicators/#keyIndicator_landIce
I. Sea level is rising. (Sea level rise is caused by the thermal expansion of sea water due to climate warming and widespread melting of land ice.)
http://www.cmar.csiro.au/sealevel/sl_hist_last_15.html
J. Ocean heat content is increasing.
http://www.nature.com/nature/journal/v465/n7296/pdf/nature09043.pdf