"Prediction is very difficult, especially about the future", goes the old saying and perhaps we should add "especially about the climate". However, it's good to work out how well past predictions have fared.
Here's a comparison of Hansen's original 1988 predictions to outcome. http://www.realclimate.org/index.php/archives/2009/12/updates-to-model-data-comparisons/
"And finally, let’s revisit the oldest GCM projection of all, Hansen et al (1988). The Scenario B in that paper is running a little high compared with the actual forcings growth (by about 10%), and the old GISS model had a climate sensitivity that was a little higher (4.2ºC for a doubling of CO2) than the current best estimate (~3ºC).
[...] Thus, it seems that the Hansen et al ‘B’ projection is likely running a little warm compared to the real world, but assuming (a little recklessly) that the 26 yr trend scales linearly with the sensitivity and the forcing, we could use this mismatch to estimate a sensitivity for the real world. That would give us 4.2/(0.26*0.9) * 0.19=~ 3.4 ºC. "There's a bit more discussion of climate sensitivity here.
The model predictions are compared to the GISTEMP and HADCRUT global temperature series. There's a great project to make the GISTEMP computer code clearer here: Clear Climate Code . The minor coding errors don't seem to have affected the temperature trend. Some will claim that the temperature trend is somewhat an artefact of Urban Heat Island Effects.
However, we also have data from satellites, showing a temperature increase in the lower atmosphere (picking UAH the more conservative of the two estimates) of 0.16 Celsius per decade. (Here's the UAH data alone).
The final source of data showing the warming trend is the ocean heat content (expressed in sensible units by David Mackay) , which shows a strong upward trend. One interesting thing about this is in the period 2000-2010, where the air temperature has been static, the sea temperature has increased a lot. The heat capacity of water (and in aggregate, the oceans) is very much greater than air, so we've actually had plenty of global warming of the oceans in the last few years.
He notes that the warming of the top 700m of oceans over the last 40 years averages about 0.45W/m2 over just the oceans. The estimated extra heat over that period is shown in this graph. This data suggests that the observed increase in heat flow is roughly two thirds of what our models suggest it should be. Therefore either estimates of fast feedback are slightly too high, or aerosol effects are larger than we expect.
In conclusion, the data suggests that global warming is happening; that models predict approximately the correct magnitude. My take on the data would be that they suggest a 'fast'/Charney climate sensitivity in the range 2-3 Celsius per doubling of CO2 concentration (to be clear, observations on ocean heat suggests towards the lower end of this range, but only if aerosols have had a relatively small effect). However, this does not include so-called slow feedbacks, such as Carbon Cycle and warming-induced Methane releases which may be significant, and therefore justify a larger range (perhaps 2-6 Celsius) for climate sensitivity.
In short, the evidence suggests that climate change is happening, that the warming is about as much as the IPCC consensus suggests, and that action is needed to not build any more greenhouse gas emitting infrastructure.